this video is sponsored by librarians
stay tuned for a special offer for arvan
ash viewers if you've had any kind of
basic chemistry class in your life
you're probably familiar with this chart
that might have scared you a little bit
when you first saw it but it's just a
list all the different types of atoms
that exist on earth it's simply arranged
based on the number of protons in the
atom's nucleus and for a neutral atom
with no charge it also has the same
number of electrons these numbers are
the main determinant of its chemical
properties
if you look more closely at this chart
you'll see that it's not just a simple
list of atoms in numerical order it is
arranged such that certain groups of
elements have similar properties
but why do these elements have similar
properties their properties have to do
with the way electrons are arranged
around the nucleus of atoms but why
should electrons be arranged this way so
specifically in certain orbitals and
shells it turns out that we have a very
powerful tool to understand why and that
tool is quantum mechanics it does
nothing less than explain the entire
periodic table of elements that is it
can account for all the atoms found on
earth how is this possible that's coming
up
right now
the structure of individual atoms and
chemistry is all about electrons how
they're arranged and shared between
atoms it all boils down to electron
shells in the precise way electrons
orbit the atom
the universe tends towards the lowest
energy state this applies to electrons
some configurations of electrons are
simply more energy efficient than others
it so happens that the lowest energy
configurations of electrons is when the
electron shells are either empty or full
what do i mean by shells to explain this
concept in a brief way let's look at the
oversimplified bohr model of the atom
bohr showed that electrons can only
exist in certain stable orbits around a
nucleus where the angular momentum is
proportional to planck's constant these
are like shells around the nucleus we
can draw the atom where the nucleus is
in the center and the rings around it
represent the electron orbits or shells
but this model of course was an
oversimplification erwin schrodinger
understood that rather than being
confined to an orbit like a planet an
electron is a matter wave that forms a
probability cloud in 3d space
smeared around the nucleus according to
quantum mechanics and he formulated the
rules to describe this behavior the
famous schroedinger equation this
equation as it turns out went beyond the
bohr model of the atom by more
accurately describing every atom that
exists in nature in other words the
structure of the entire periodic table
of the elements can be predicted by
schrodinger's equation this was nothing
short of astounding
the schrodinger equation showed that
each shell has a maximum number of
electrons it can hold the innermost
shell holds a maximum of two electrons
the second holds a maximum of eight
electrons the next up to 18 then 32 then
50 and so on
chemistry is about substances exchanging
or sharing electrons in order to fully
fill up these shells
okay so now the elephant in the room
that needs explaining is
why are these numbers so special
these numbers look random why in the
world do atomic interactions care about
conforming to these numbers it all comes
down to energy
systems in the universe tend towards
their lowest energy state to minimize
energy the electrons fill up the orbits
starting from the center and moving out
and it turns out that having full or
empty orbitals minimizes the energy of
the atom
to understand why we have to solve the
schrodinger equation although this
equation looks intimidating and it can
be in its essence is just a statement of
energy conservation it simply says that
total energy is equal to potential
energy plus kinetic energy that's it
this equation can be solved most easily
for the hydrogen atom because it is the
simplest atom just one electron orbiting
one proton because the core is made of
just one proton it's spherically
symmetrical if you imagine the proton
like a ball it doesn't matter how you
rotate it it always looks the same it
has symmetry if we consider something
like hydrogen 2 also called deuterium
which has a proton and neutron in the
nucleus it would no longer be
spherically symmetrical because if you
rotate the nucleus the neutron would
point in a different way
this spherical symmetry is essential for
making the solution simple enough to
solve the schrodinger equation exactly
now i don't want you to get intimidated
by this equation i just want you to get
familiar with it so that you can
understand where the electron shell
numbers are coming from
in the schrodinger equation we have a
kinetic energy term and a potential
energy term that we define
because hydrogen has a positively
charged nucleus and a negatively charged
electron there's an attractive coulomb
potential between the electron and the
proton this is where the potential
energy term comes from
there's several constants in this
equation that we don't have to solve for
as shown here planck's constant epsilon
or the vacuum permittivity mass of
electron and proton and e the electric
charge constant i won't derive this
equation in this video because that's
not important for understanding the
subject we're covering today the key
term to look at here is psi
this is the term we have to solve for it
is the wave function of the hydrogen
atom it represents a value that is
related to the probability of this atom
being in certain quantum states the
radius and angles theta and phi
represent the spherical coordinates of
our system in three-dimensional space
now even though this is the simplest
atom to solve for it's still quite
difficult to do but solving for the wave
function of the hydrogen atom gets you
the following result
this equation is a bit of a mouthful and
it takes many pages and hours of work to
derive but let's look at some of the
components so that you can understand
how this plays a role in the shells
around the nucleus
the main thing i want you to look at are
these three extra labels
n l and m
where did these come from when solving
the schrodinger equation you get a set
of complicated differential equations in
order to solve these you have to
specify some quantum values for the atom
these are values or quantities that have
to be inserted in the equation to solve
for psi
i have a link to the long solution if
you want to see how this is done
n just represents the electron shell
layer
n equals 1 is the ground state or the
lowest energy state of the hydrogen atom
but hydrogen is not always found in its
lowest energy state so it can take on
other values l is a quantum number
defining the orbital angular momentum
and m is the number which specifies the
orientation and space of the orbital
now here's the key to the significance
of this equation when we plug in
different values for n l and m in the
schrodinger equation for the hydrogen
atom it also approximately represents
the solution to all the quantum states
of electrons for any other atom so this
equation allows us to predict how
electrons behave for all the elements of
the periodic table
now there are some rules for choosing
the numbers n must be an integer
starting with one
since it specifies the shell there is no
such thing as a 1.5 shell or 1.3 shell
the shells can only be 1 2 3 and so on
depending on the value of n
l will be an integer from 0 to n minus
1.
and finally the value of m depends on
the value of l this can be integer
values between negative l
and positive l
for example if n equals 1 then we must
have that l equals 0 and thus m equals
0. if n equals 2 l can equal 0 or 1 and
m can equal negative 1 0 and 1. if n
equals 3 then we can have l equal to 0
one or two and m equals
negative two negative one zero one and
two in that case
and this pattern continues
now let's try to visualize it
let's consider the case where n equals
one this is the atom in its ground state
l and m are zero in this case the result
is a spherical wave function it's just
like a small fuzzy ball the schrodinger
equation in this case indicates that the
probability of finding the electron
is in a spherical cloud around the
nucleus what if we solve for the case
where n equals two a higher shell and l
and m are still both zero in that case
the atom would be adding another shell
around the first shell in fact if we
keep l and m zero then as we consider n
equals three four and so on we just add
more shells around the nucleus now what
if we set n equals to two keep l equal
to zero like before but also l could
equal one
in the latter case m can be either
negative one zero or one
thus we would have one configuration
with l equal to zero and three
additional configurations with l equal
to one
so if we add all these configurations we
would have a total of four
configurations for the case where n
equals two let's now compare this to the
rows of the periodic table
the first row has two elements and the
second row has eight elements
if n equals one we know that we can have
one configuration and if n equals two we
know that we have four configurations
this looks similar to the possible
electron shells in the atom except that
it's double eight instead of four and
two instead of one
it turns out these quantum numbers are
explaining the possible shells or
orbitals available to the electrons but
then what about this factor of two where
does this come from here's where you
have to remember that electrons are spin
one-half particles this means they can
be spin up or spin down
the polyexclusion principle says that
you can't have two fermions the ferbians
are electrons in this case with the same
quantum numbers in the same place
but you can have a spin up and spin down
for each choice of n l and m
and because the spins are different they
would not be identical this is why we
have two electrons per configuration
so although the schrodinger equation
shows four configurations for n equals
one and n equals two we can double it to
eight configurations since we can have
four electrons that spin up and 4 more
electrons would spin down similarly if
we solve for n equals 3 n equals 4 etc
we find that the total number of
configurations is equal to the electron
shell numbers i showed at the beginning
of the video so the structure of the
periodic table
can be understood just by solving the
schrodinger equation for the hydrogen
atom but you might ask why don't we need
to solve the schrodinger equation for
helium or sodium or uranium to be really
sure that the orbits are correct can the
hydrogen solution really work for all
atoms
well the answer is no not quite this
hydrogen solution isn't exactly correct
it gets less accurate for larger atoms
so if you look at it in detail there's
some small variations for the larger
atoms and in those cases the orbits can
be occupied in a slightly different way
but the problem is that the schrodinger
equation becomes so unwieldy for large
atoms that it cannot be solved but since
we can solve it exactly for hydrogen it
can give us a very good understanding
for other atoms nevertheless there are
also some details that i'm skipping over
for example the orbits associated with a
higher value of l are not necessarily
the shells with the next lowest energy
this is why for example you learned in
chemistry that instead of starting the d
orbit in the third row you start with
the next s orbit the reason is because
the schrodinger equation shows that when
n equals four and l equals zero in the s
orbit it is actually more energy
efficient than at the d orbit
but after that it becomes more efficient
to fill up the d orbits so simply put
depending on the quantum numbers of the
wave function you fill up the orbits in
terms of what requires the least energy
and voila
you get the periodic table
at the end of the day chemistry is just
quantum mechanics with electrons so i
hope this helped you finally understand
why the periodic table looks the way it
does and has to look the way it does
if you want to explore further and learn
more about the periodic table of
elements one of the best courses on this
subject is available on one dream hit a
sponsor called understanding the
periodic table taught by professor ron
davis of georgetown university his
course not only explores the information
contained in this iconic chart but also
goes deeper he answers interesting
questions such as why does neon make for
such great lighting how do nitrogen and
oxygen balance earth's atmosphere for
life and why are copper silver and gold
the colors that they are you can not
only enjoy these great lectures by
professor davis but also some of the
best educators in the world you'll be
hard-pressed to find a better online
learning service than one dream this is
why i've been a member for a long time i
couldn't recommend them more you'll even
see my testimonial at the bottom of one
dream's home page it's really easy to
sign up right now because they are
offering a free trial and you can cancel
at any time so you have nothing to lose
but a lot to gain if
have any questions or comments from me
or other viewers please leave them in
the comment section i try to look at all
of them i'll see you in the next video
my friend
[Music]
[Applause]
[Music]
[Applause]
[Music]
you