Understanding the Atom
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Includes: Chapter 1: Protons, Neutrons, Electrons, Strong Nuclear Force, Ions, Cations, Anions, Mass Number, Atomic Mass, Atomic Number, Isotopes, Nucleus, and Relative Size of Atom, Many Examples and Calculations Worked for the Student. Chapter 2: Quantum Theory, Orbits vs. Orbitals, Orbital Shapes, Electron Configuration Diagram. Chapter 3: Writing Full Electron Configurations and Diagrams, Aufbau Rule, Hünd's Rule, Pauli Principle, and Connection between Periodic Table and Order of Filling for Electrons, Many Examples Worked for the Student. Chapter 4: Writing Abbreviated Electron Configurations and Diagrams, Noble Core and Valence Electrons, Many Examples Worked for the Student. Chapter 5: Determining the Four Quantum Numbers (Principle, Angular Momentum, Magnetic, and Spin Quantum Number), Many Examples Worked for the Student. Narration: William R. Sponholtz, III, B.S., M.S., PH.D. The DVD version is available at https://sponholtzproductions.com
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[Music]
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if everything in the known universe is
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composed of atoms then we should all
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have a basic understanding of the atom
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and the three fundamental subatomic
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particles the proton the neutron and the
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electron therefore the goal of this
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chapter is to define and deduce the
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number of protons neutrons and electrons
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that an atom possesses and understand
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where these subatomic particles reside
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within an atom there is a great deal of
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information that can be gleaned from the
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periodic table in fact many refer to the
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periodic table as the world's greatest
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cheat sheet for example what makes
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helium different from all the other
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elements found within the periodic table
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examining helium closer we see that the
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atomic number for helium is 2 the atomic
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number indicates how many protons are
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found in the nucleus of an atom
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thus elemental identity comes from the
01:10
number of protons in other words for
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helium to be helium and must possess
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only 2 protons if helium gained a proton
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the atomic number would become 3 which
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means it's elemental identity would also
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change from helium to lithium the two
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protons of helium exists at the center
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of the atom called the nucleus and each
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proton has a positive charge the two
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similar positive charges should repel
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each other what an attractive force
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called a strong nuclear force helps to
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overcome this repulsion and the two
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subatomic particles are actually
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attracted to each other
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it should be noted that this attraction
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only occurs at the subatomic level
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the repulsions are further reduced with
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the help of neutrons the neutrons are
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also found inside the nucleus which are
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slightly heavier than the protons and
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have no charge it may help to think of a
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neutron as nuclear glue that increases
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the extent of the strong nuclear force
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which helps hold the protons together
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the sum of the protons and neutrons is
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referred to as the mass number in this
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example helium has two protons and two
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neutrons thus the mass number is four
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which is often given in the upper
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left-hand corner of the element and the
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atomic number is two which appears in
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the lower left-hand corner
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however the atomic number is often
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omitted after all atomic number can be
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deduced from the periodic table if the
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elemental symbol is given for example
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the atomic number in the lower left-hand
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corner does not have to be included for
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carbon if we have access to a periodic
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table from the periodic table we see
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that carbon has an atomic number of six
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thus there are six protons present to
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deduce the number of neutrons we simply
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subtract the number of protons from the
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mass number thus there are six neutrons
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remember the mass number is the sum of
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the neutrons and the protons at this
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point we can introduce isotopes isotopes
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are atoms with the same number of
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protons but different number of neutrons
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for example the two common isotopes of
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carbon are carbon-12 and carbon-13 they
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both have the same number of protons six
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but the number of neutrons are different
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carbon-12 has six and carbon-13 has
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seven neutrons which were deduced from
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subtracting the number of protons from
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the mass number
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now let's look at two isotopes of
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chlorine and deduce their numbers of
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protons and neutrons here again the
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atomic number in the lower left-hand
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corner has been omitted because we have
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access to a periodic table examining the
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periodic table we see that chlorine is
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atomic number 17 thus both isotopes have
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17 protons the mass numbers 35 and 37
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then allow us to deduce the number of
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neutrons for each isotope 18 and 20 the
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fractional abundance of the chlorine 35
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isotope is seventy five point five three
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percent and the fractional abundance of
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the chlorine 37 isotope is twenty four
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point four seven percent put another way
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in any sample of pure chlorine seventy
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five point five three percent of the
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sample is the chlorine 35 isotope and
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twenty four point four seven percent is
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the chlorine 37 isotope now let's use
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this data to introduce the atomic mass
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of an element the atomic mass of an
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element is the weighted average of the
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masses of the naturally occurring
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isotopes but what are the masses of each
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isotope and how are they calculated to
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answer this question we need to
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introduce the atomic mass unit or a mu a
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protons actual weight is a fraction of a
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gram
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thus it is easier if we simplify this
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value to one atomic mass unit although a
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neutron is slightly heavier than a
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proton we will also simplify this value
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to 1 amu taking the weighted average of
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the two chlorine isotopes means we have
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to account for the fractional abundance
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of both of these isotopes
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thus the chlorine-35 isotope is the
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major isotope and its mass needs to be
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accounted for approximately 75% of the
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time while the mass of the minor isotope
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3/7 needs to be accounted for
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approximately 25% of the time for
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simplicity we have rounded the
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fractional abundances and masses for
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both isotopes within our calculations as
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we expected the atomic mass 35.5 amu
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lies closer to the mass number of the
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more abundant chlorine-35 isotope in the
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previous carbon example we examine two
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isotopes of carbon the carbon 12 isotope
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is the major isotope and its mass needs
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to be accounted for ninety eight point
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eight nine percent of the time while the
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mass of the minor isotope carbon-14
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needs to be accounted for one point one
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one percent of the time as we expected
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the atomic mass for carbon twelve point
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O one amu lies much closer to the mass
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number of the more abundant isotope thus
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the atomic mass of an element depends on
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both the mass and the relative abundance
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of each of the elements isotopes the
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third subatomic particle the electron is
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a negatively charged particle that
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resides outside of the nucleus within
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orbitals in the next chapter we'll
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examine orbitals in much more detail but
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for now we will simply focus on how to
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ascertain the number of electrons that
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an atom possesses and how it affects the
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charge of the atom the actual charge
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that the positively charged proton and
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negatively charged electron possesses is
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very small
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thus for simplicity we will assign a
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positive 1 and a negative 1 charge to
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these subatomic particles if there are
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the same number of electrons as protons
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all charges will cancel and the atom
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will have no charge however if a
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different number of electrons than
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protons exists within an atom then the
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atom will have a charge called anion and
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this charge is written in the upper
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right-hand corner if an atom has more
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electrons than protons this ion is
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called an anion which has a negative
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charge and if an atom has less electrons
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than protons
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this ion is called a cation which has a
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positive charge
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for example if carbon gained an extra
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electron there would be one more
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electron than protons thus it would have
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seven electrons and a negative one
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charge
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in the next couple of examples it may
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help to think of an anion as an atom
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that has gained electrons and a cation
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as an atom that has lost electrons from
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the information given we do not need to
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consult a periodic table to deduce the
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number of protons for the fluorine 19
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anion however if the atomic number of
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nine was not given we could have simply
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found fluorine on the periodic table and
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deduced its atomic number thus there are
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nine protons the number of neutrons is
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calculated from subtracting the number
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of protons from the mass number which
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gives 10 neutrons the negative one
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charge indicates there is one extra
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electron when compared to the number of
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protons thus there are 10 electrons
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here the atomic number of 12 is given
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for the magnesium 24 cation thus there
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are 12 protons again the number of
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neutrons is calculated from subtracting
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the number of protons from the mass
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number which affords 12 neutrons and
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finally the positive 2 charge indicates
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we have lost 2 electrons when compared
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to the number of positive charges thus
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there are 10 electrons this is always a
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good idea to check your work
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for example if you deduced there was 12
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protons and 10 electrons you can simply
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add them together 12 positives with 10
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negatives adds 2 plus 2 which matches
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the charge of this cation it is
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important to be able to quickly deduce
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the quantity of each of these subatomic
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particles so that you can gain a better
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understanding of the atom you are
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examining in fact different atoms have
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distinct chemical properties and
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reactivities due to the different
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numbers of protons neutrons and
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electrons now that we have developed
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skills to deduce numbers of protons
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neutrons and electrons for any isotope
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or ion let us start to get a feel for
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the relative sizes of these particles
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within an atom we have already learned
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that the proton is positively charged
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and the neutron has no charge that they
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both reside within the nucleus are about
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the same size and they are both
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approximately 2,000 times bigger than a
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negatively charged electron which
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resides in an orbital the term nucleus
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loosely translates to little nut in
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Latin
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[Music]
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so how small is the nucleus compared
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with the size of the orbital where the
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electron resides imagine you are
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standing in the middle of one half of a
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soccer field and you were holding a
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grain of rice in your hand which
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represents the size of a proton in this
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analogy now imagine the size of an
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electron which is one mm the size of
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that grain of rice this very small
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particle our electron moves rapidly and
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randomly inside this giant sphere with a
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fixed amount of energy this giant sphere
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is called an orbital which is the whole
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half of the field above and below you
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this is what an atom of hydrogen is like
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as you can see an atom is a whole lot of
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empty space even more in mind-boggling
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is the fact that an atom is so small
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that a human hair is approximately 1
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million carbon atoms in width
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[Music]
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in the early 1900's many brilliant minds
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were changing the landscape of science
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in particular quantum theory was
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emerging and changing the way we viewed
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the atom one of the great results of
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quantum mechanics was the orbital which
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is where the electrons reside an orbital
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should never be confused with an orbit
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an orbit is a mathematically defined
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pathway for example how the Earth orbits
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the Sun using classical Newtonian
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physics we can predict where the earth
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will be on the orbit at some time T and
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where it was at some time T in the past
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you may have seen a similar simplified
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model of the atom where the electron is
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orbiting the nucleus on a mathematically
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defined pathway which couldn't be
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further from the truth an orbital is a
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much more complicated concept than an
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orbit in fact we know nothing about how
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the electron moves around the nucleus
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thus quantum mechanics demonstrated that
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electrons did not move around in neat
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orbits but existed in regions called
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orbitals with a fixed amount of energy
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in simplest terms an orbital is a
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three-dimensional region or shape and
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you can expect to find an electron
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inside the shape 90% of the time and may
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help to think of this shape as a
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boundary surface the electron is more
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likely to be inside this boundary shape
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rather than outside the boundary let's
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apply this concept of boundary shape to
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the electron of the hydrogen atom which
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has one proton in the nucleus and one
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electron in a surrounding orbital if you
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imagine the electron is moving in a
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random manner with fixed energy around
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the nucleus and then imagine that we
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take a picture of this electron every
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second for a day a week or month
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you see that all these pictures laid on
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top of one another
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begin to form an electron cloud around
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the nucleus remember all these
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hypothetical pictures or data points
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represent where the electron has been
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over time if we now attempt to create a
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three-dimensional surface to encompass
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90% of all these data points we obtain a
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sphere which is often called the
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boundary surface the creation of this
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boundary surface for the hydrogen atom
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which is called an S orbital requires
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some pretty complex calculus thus if an
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electron is in an orbital the electron
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has a fixed amount of energy and the
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orbital is a three-dimensional region
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around the nucleus that indicates the
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probable location of that electron 90%
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of the time there are many different
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orbitals for the electrons to reside the
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success of solutions or orbitals from
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quantum mechanics increase in relative
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energy when we add the shapes to the
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energy turns we get the following
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electron configuration diagram which
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shows all the orbitals available for
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electrons to reside the orbitals fall
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into one of four broad categories s P D
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and F orbitals interestingly there is
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one solution each time an S orbital is
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obtained three solutions of the same
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energy each time a P solution is
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obtained five solutions are the same
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energy each time a D solution is
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obtained and seven solutions of the same
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energy each time an F solution is
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obtained in the next chapter we will
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revisit this diagram in detail to aid in
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writing electron configurations for now
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let's just focus on what this diagram
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represents the orbitals and each of
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these lines abstractly represents an
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orbital for example the first line on
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the electron configuration diagram is
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the 1s orbital and it is a sphere this
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is where the first two electrons of an
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atom can be found 90% of the time
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in addition all of the s orbitals are
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shaped like fears the three 2p orbitals
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are shaped like dumbbells oriented along
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the three axis the 2px 2py and 2pz for
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convenience your instructor will often
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shrink them down to a third of their
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size so that they are easier to draw if
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we continue to go up and relative energy
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the shapes of the orbitals become
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increasingly more complicated as
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demonstrated by the 3d orbital shapes
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and it is unlikely that your instructor
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will hold you accountable before these
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shapes although this diagram may look
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complicated remember that each line
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abstractly represents an orbital and
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that all these orbitals overlap on the
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same atom here you can see that a 1s
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orbital is the first orbital that the
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electrons will reside in then the 2's
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orbital is on top of that then the three
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2p orbitals on top of them and so on and
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so on until the necessary amount of
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orbitals are present to house all of the
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electrons that an atom may possess if
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orbitals are where electrons can be
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found 90% of the time in the next
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chapter we will examine how many
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electrons are in each orbital and the
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order in which they are filled by an
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atom
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[Music]
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the arrangement of electrons in an atom
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is known as the atoms electron
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configuration think of this as finding a
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home for each electron electrons want to
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be in the lowest energy arrangement
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called the ground state electron
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configuration and to accomplish this we
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need to follow three basic rules the
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off-ball principle tells us the order
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the orbitals are filled
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alfe ball is a german word meaning to
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build up just like building a house we
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need to start at the bottom floor when
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that is completely finished we begin on
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the next floor thus electrons are added
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to the lowest energy orbital first and
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then we work our way up in relative
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energy this means that on the electron
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configuration diagram electrons are
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placed into the 1s orbital first then
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the 2s followed by the 2p 3s 3p and so
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on and so on until the necessary amount
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of orbitals are filled to house all the
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electrons that an atom may possess the
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next rule is called the Pauli exclusion
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principle which simply translates to
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only 2 electrons per orbital with
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opposite spin within the electron
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configuration diagram we will represent
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electrons as 1/2 arrows the first arrow
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is up and the second arrow is down
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remember that each line on this diagram
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abstractly represents an orbital and
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that each arrow represents an electron
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in that orbital below the diagram is the
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electron configuration notation which
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utilizes exponents to indicate the
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number of electrons within each orbital
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the third and last rule is called hoons
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rule which states orbitals of equal
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energy are occupied by one electron
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before any orbital is occupied by a
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second electron now let's review these
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three basic rules the first electron
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goes into lowest energy orbital 1s
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orbital which is the Aufbau rule the
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second electron goes into that same
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orbital with opposite spin the Pauli
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exclusion principle states we can only
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have two electrons per orbital thus the
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third electron goes into the next
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highest energy orbital the two
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the fourth electron also goes into the
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2's orbital but with opposite spin
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followed by the fifth electron filling
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one of the 2p orbitals hoon's rule
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states that the six electron will go
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into a different 2p orbital because we
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should fill the orbitals one at a time
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across an energy level before pairing
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electrons subsequent electrons are added
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following these three basic rules until
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the required amount of electrons are
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added to work this example problem we
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first need to consult the periodic table
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to ascertain how many electrons are in a
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neutral atom of carbon in the first
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chapter we learned how to quickly deduce
20:39
the number of electrons and we will need
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this skill now the atomic number of
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carbon is 6
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thus a neutral atom of carbon has 6
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electrons therefore this problem simply
20:51
translates to finding a home for 6
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electrons following our three simple
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rules we place all six electrons into
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our diagram as shown start at the bottom
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working our way up two electrons per
21:04
orbital with opposite spin and fill the
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orbitals one at a time across an energy
21:08
level before pairing electrons
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in this example we have one more
21:23
electron than the atomic number of
21:25
fluorine
21:25
thus examining the periodic table we see
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that fluorines atomic number is nine
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which means there are nine protons and
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ten electrons if we have a negative one
21:34
charge thus the problem is really asking
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us to find a home for 10 electrons again
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following our three simple rules we
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place all 10 electrons into our diagram
21:45
as shown in this example the calcium
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atom has lost two electrons when
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compared to the number of protons
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thus examining the periodic table we see
22:01
the calcium città McNutt wente which
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means there are 20 protons and 18
22:06
electrons if we have a positive 2 charge
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thus the problem is really asking us to
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find a home for 18 electrons again
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following our three simple rules we
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place all 18 electrons into our diagram
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as shown
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[Music]
22:34
first we need to consult the periodic
22:37
table to ascertain how many electrons
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are in a neutral atom of gallium which
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will be the same as the atomic number
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for gallium gallium atomic number is 31
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which means there are 31 electrons if
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gallium has no charge thus the problem
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is really asking us to find a home for
22:56
31 electrons again following our three
22:59
simple rules we place all 31 electrons
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into our diagram as shown
23:06
[Music]
23:16
you are probably thinking that it is
23:18
going to be very challenging to memorize
23:20
and reproduce the electron configuration
23:23
diagram template shown however if you
23:25
have access to a periodic table you can
23:28
easily reproduce it for example if you
23:31
simply read the periodic table from left
23:33
to right the correct order of orbital
23:36
filling is obtained 1s 2s 2p 3s 3p 4s
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then you go down a level for the 3d back
23:49
up to the 4p 5s down a level for the 4d
23:53
and so on in addition the periodic table
23:56
tells us how many electrons go into each
23:59
sublevel for example the s block is 2
24:03
elements across the Stu electrons can go
24:05
into all the s sub levels the P block is
24:09
6 elements across the 6 electrons can go
24:12
in all the P sub levels the D block is
24:16
10 elements across thus 10 electrons can
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go in all the D sub levels and finally
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the F block is 14 elements across which
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means 14 electrons can go in all the F
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sub levels you may notice that when we
24:32
compare the order of filling we obtained
24:35
from the periodic table to the electron
24:37
configuration diagram template they are
24:39
the same clearly having access to a
24:42
periodic table helps us reproduce the
24:44
electron configuration diagram template
24:47
thus you should practice drawing this
24:49
diagram on your own with the aid of a
24:51
periodic table until you have mastered
24:53
this skill
24:57
as you can tell the keys to writing
24:59
electron configurations are to quickly
25:01
ascertain the number of electrons for an
25:03
atom or ion from the periodic table and
25:06
to be able to quickly reproduce the
25:09
template for the electron configuration
25:10
diagram remember you can use the
25:14
periodic table to help you reproduce it
25:16
then simply follow the three basic rules
25:18
for electron configurations and you
25:21
should have no problems determining
25:22
electron configurations
25:26
[Music]
25:41
in the last chapter it may have seemed
25:43
difficult representing electron
25:45
configurations and drawing the full
25:47
electron configuration diagrams for
25:49
atoms that possessed many electrons for
25:51
example the 31 electrons that are found
25:54
in a neutral atom of gallium fortunately
25:57
there is a much easier way abbreviated
26:00
electron configurations allows to
26:01
combine the inert noble core electrons
26:04
with the remaining outermost electrons
26:06
therefore to be able to write the
26:09
abbreviated electron configuration we
26:11
need to first become familiar with noble
26:14
core electrons the noble core electrons
26:18
have the same electron configuration
26:19
often termed isoelectronic as a noble
26:23
element to better understand noble core
26:25
electrons let's return to the previous
26:27
gallium example recall the galleons
26:31
atomic number was 31 which meant we
26:34
found a home for the 31 electrons of a
26:36
neutral atom of gallium the noble
26:39
elements are the last family on the
26:41
periodic table to abbreviate the noble
26:44
core electrons for gallium we simply
26:47
slide back until we reach the first
26:49
noble element which is argon argon has
26:52
18 electrons thus we can abbreviate the
26:55
first 18 electrons of gallium as the
26:58
element argon these 18 electrons begin
27:03
at the 1s and end at the 3p orbital and
27:06
are represented by the noble element
27:09
argon in brackets clearly the
27:12
abbreviated diagram is much easier to
27:14
draw than the full electron
27:16
configuration diagram
27:17
[Music]
27:24
in this example we will first draw the
27:28
full electron configuration diagram for
27:30
a neutral atom of potassium then we will
27:33
focus on the abbreviated versions
27:38
potassium città Makhno 19 which means
27:42
there are 19 electrons for a neutral
27:43
atom of potassium
27:45
following the Alpha rule Pauli exclusion
27:47
principle hoons rule the following
27:50
diagram and electron configuration is
27:53
quickly obtained for the 19 electrons of
27:55
potassium to abbreviate the noble core
28:00
electrons for potassium we simply slide
28:02
back until we reach the first noble
28:04
element which is argon with 18 electrons
28:07
thus we can abbreviate the first 18
28:10
electrons of potassium as the element
28:13
argon the first 18 electrons of
28:17
potassium which begin at the 1s and
28:19
ended the 3p orbital are represented by
28:21
the noble element argon in brackets the
28:27
remaining electron in the 4s orbital is
28:30
the outermost electron commonly called
28:32
the valence electron it is often very
28:34
important to quickly ascertain the
28:36
number of valence electrons than an atom
28:38
possesses after all these are the
28:41
electrons that will be involved in bond
28:43
making and bond breaking the noble core
28:47
electrons will not be involved in bond
28:49
making and are often called the inert
28:51
noble core electrons thus let's focus
28:54
our efforts on the reactive valence
28:57
electrons
28:59
to answer how many valence electrons
29:02
carbon has we will first write the
29:04
abbreviated electron configuration we
29:07
see that a neutral atom of carbon has
29:09
six electrons thus the electron
29:11
configuration for the six electrons of
29:14
carbon is 1s2 2s2 2p2 however we need to
29:20
write the abbreviated electron
29:22
configuration to answer this question
29:24
thus we slide back to the nearest noble
29:26
which is helium helium will represent
29:29
the two noble core electrons which
29:32
leaves four valence electrons it should
29:35
be noted that we did not have to draw
29:37
the full or the abbreviated electron
29:39
configuration diagram to answer this
29:41
question we just needed access to a
29:44
periodic table for example if we first
29:48
slide back to the nearest noble which is
29:50
helium then we can simply count forward
29:53
to the element in question and that will
29:55
equal how many valence electrons that
29:57
atom possesses one two three four
30:02
valence electrons which matches our
30:04
result from drawing the electron
30:06
configurations
30:08
[Music]
30:10
let's try to answer one more of these
30:13
questions using only the periodic table
30:15
for phosphorous for example if we first
30:19
slide back to the nearest noble which is
30:21
neon then we can simply count forward to
30:24
the element in question and that will
30:26
equal how many valence electrons that
30:28
atom possesses which is five valence
30:30
electrons thus from the periodic table
30:34
we see that there are ten noble core
30:35
electrons which we could represent by
30:38
placing neon and brackets and the
30:40
remaining five valence electrons are
30:42
placed into the 3s and 3p orbitals which
30:46
matches the diagrams shown having the
30:56
ability to quickly ascertain the number
30:58
of valence electrons and atom has is
31:01
very important in bonding theory which
31:03
is thoroughly examined in the next DVD
31:05
of this series introduction to bonding
31:08
[Music]
31:16
the four quantum numbers are a direct
31:18
result from various quantum mechanical
31:20
equations these four quantum numbers
31:23
completely describe where an electron
31:25
can be located in a more simplified view
31:28
one could say that the four quantum
31:30
numbers give rise to the solutions or
31:33
orbitals that the electrons occupy or
31:37
that they give rise to the electron
31:39
configuration diagram shown which was
31:41
covered in Chapter two
31:43
while thorough treatment of this topic
31:45
is beyond the scope of this DVD your
31:47
instructor may ask you to assign the
31:50
four quantum numbers to an electron
31:51
thus it is worth our efforts to learn
31:53
about the four quantum numbers the four
31:56
quantum numbers are the principal
31:58
quantum number which will tell us the
32:00
energy level the electron is located the
32:03
angular momentum number which will
32:05
indicate the shape of the orbital the
32:07
magnetic quantum number which indicates
32:09
on which axis the orbital is on and the
32:13
spin quantum number which has only two
32:15
possible values plus 1/2 which is up or
32:19
minus 1/2 which is damn while this may
32:23
seem confusing it is actually very easy
32:25
to assign the four quantum numbers to an
32:27
electron as the following examples we'll
32:30
demonstrate
32:33
[Music]
32:37
after we draw the electron configuration
32:39
diagram for nitrogen we see that the
32:42
last electron occupies a 2p atomic
32:44
orbital thus the principal quantum
32:47
number which represents the energy level
32:49
is 2 the second quantum number the
32:53
angular momentum number represents the
32:56
shape of the orbital and from the chart
32:58
if the electron is in a p orbital l is
33:01
equal to 1 the third quantum number the
33:06
magnetic quantum number M have the
33:09
designations shown from minus L to plus
33:12
L thus this electron in the last 2p
33:16
orbital has the value of +1 and the last
33:22
quantum number which indicates the spin
33:25
of the electron is plus 1/2 because the
33:27
electron is pointing up thus the four
33:30
quantum numbers are 2 1 plus 1 and plus
33:34
1/2
33:37
[Music]
33:41
in the next example we are asked to
33:44
assign the four quantum numbers to the
33:45
last electron of a chloride anion from
33:49
the electron configuration diagram we
33:51
see that we need to fully describe the
33:53
last three P electron the electron is in
33:57
the third energy level thus and is three
34:00
it occupies a p orbital thus L is 1 M is
34:07
+1 and the electron is pointing down
34:11
therefore it is minus 1/2 thus the four
34:14
quantum numbers are 3 1 plus 1 and minus
34:18
1/2 in the next example we are asked to
34:26
assign the four quantum numbers to the
34:28
last electron of an atom of titanium
34:30
from the electron configuration diagram
34:33
we see that we need to fully describe
34:35
the second 3d electron the electron is
34:39
in the third energy level thus and is 3
34:42
it occupies a D orbital thus L is 2 M is
34:48
minus 1 and the electron is pointing up
34:52
therefore it is plus 1/2 thus the four
34:55
quantum numbers are 3 2 minus 1 and plus
34:59
1/2 if chemistry is considered to be the
35:05
central science than having a basic
35:07
understanding of the atom and the three
35:10
fundamental sub atomic particles the
35:12
proton the neutron and the electron is
35:15
essential after all
35:17
the student who has the ability to
35:19
understand the atom can take the next
35:21
crucial steps to comprehend many
35:24
different aspects of chemistry
35:25
[Music]
English (auto-generated)