hello and welcome to the chemistry
solution this tutorial covers electron
configurations including Hans rule and
the Pauli exclusion principle first
let's talk about orbitals shells and
subshells quantum mechanics describes
the probability of finding an electron
in space using wave functions and unless
you end up taking physical chemistry in
college you really don't need to know
much more about this process but the
quantum mechanical model uses three
numbers to describe an orbital the first
is n and n is equal to the energy level
or shell and it's in these energy levels
that the sub shells and orbitals reside
now the energy level has an integer
value starting with 1 the second quantum
number is L and that's equal to the
shape or sub shell of an orbital and so
L can have any value from 0 to n minus 1
and the shapes of orbitals are denoted s
P D and F and we'll talk about those
more in just a minute
M sub L is equal to the orientation and
space of an orbital and so the value for
M sub L ranges from negative L all the
way to positive L now I said that the
shapes we refer to our s P D and F S sub
shells have only one orientation in
space P sub shells have three
orientations these sub shells have 5 and
S sub shells have seven orientations in
space now each orbital can hold two
electrons with opposite spins and we
denote these as plus 1/2 or minus 1/2
and this is used as the fourth quantum
number to describe an electron now this
might seem very confusing so let me
recap now that I've kind of told you
what all these numbers are first you
have the shells and these are the energy
levels inside each cell
you have sub shells and these sub shells
have different shapes s P D and F inside
each sub shell you have orbitals and
each orbital can hold two electrons so
because the s subshell has only one
orientation that means there is one
orbital in the s subshell and that
orbital can hold two electrons because
the p subshell has three orientations in
space that means in the p subshell
there are three different orbitals and
each one of those three orbitals can
hold two electrons giving the p subshell
at the capacity to hold six electrons
and likewise the d subshell has five
different orientations which means there
are five D orbitals and each of those
orbitals can hold two electrons for a
total of ten and each F sub shell has
seven orientations meaning it to hold
seven orbitals or fourteen electrons
this will become a little more clear as
we start diagramming our electron
configurations let's start by drawing
out the electron configurations for the
first six elements on the periodic table
hydrogen has one electron helium two
lithium three Brillion for boron five
and carbon six electrons so for hydrogen
we need to diagram one electron you
always start with the one s subshell one
denotes the energy level and s denotes
the sub shell so we'll draw the electron
like a half arrow now let's look at the
electron configuration for helium we
need to diagram two electrons remember
that each orbital can hold two electrons
so we draw in the first electron and
then whenever you're going to pair up
electrons in orbitals they need to have
opposite spins so we diagram the second
electron as an upside-down half arrow
and this denotes that the two electrons
have opposite spins and what the Pauli
exclusion principle states is that no
two electrons in the same orbit
can have the same spin or no two
electrons can have the same four quantum
numbers so if you go back to that
previous slide you'll see that the
fourth quantum number was denoted by the
spin of the electron M sub s as either
plus 1/2 or minus 1/2 so in any given
orbital your electrons need to have
different spins let's try the electron
configuration for lithium will again
start with the one s subshell it can
hold two electrons we always place
electrons in the lowest energy orbitals
first so you always place electrons in
the 1s orbital first if you go back to
the previous slide you'll notice that
the value for the sub shell or L the
shape of the sub shell has a value from
0 to n minus 1 and so the energy level
one can only hold the S sub shell now
that that sub shell is filled we need to
go up an energy level to the two s sub
shell and we have one more electron for
lithium so we place that in the to S sub
shell now let's draw the electron
configuration for beryllium again we
start with the one s subshell putting in
electrons with opposite spins and
continue to the two s subshell first
place in our third electron and just
like we did with the one s subshell
placing our fourth electron in the 2's
orbital with an opposite spin moving to
boron we place our first two electrons
in the 1s sub shell then we place our
second two electrons in the 2's sub
shell but for the N equals two shell you
have not only the s subshell but you
also have the P sub shell so remember
that the P sub shell contains three
orbitals each with a different
orientation in space and so our fifth
electron goes into one of the unoccupied
2p orbitals now let's draw the electron
configuration for carbon start with the
1s place in our two electrons with
opposite spins then the to s again
electrons with opposite spins and then
the 2p you
place our first electron in one of the
unoccupied 2p orbitals and when we go to
place the sixth electron instead of
immediately pairing it up we place it in
one of the unoccupied 2p orbitals so
Hans rule says if four orbitals of the
same energy or degenerate orbitals
electrons with the same spin will singly
occupy each orbital before pairing up so
as I was drawing my electron
configurations here I was going from
lowest to highest energy one at the 1s
orbital having the lowest energy
followed by the 2's orbital followed by
the 2p orbitals which are all equal in
energy or degenerate orbitals that means
that as I place my electrons in the 2p
orbital I maintain the same spin and put
one electron in each orbital before
pairing them up we can then write our
electron configurations in an
abbreviated fashion by writing the
energy level and sub shell followed by
the number of electrons in that sub
shell as a superscript so for hydrogen
we would write that 1s one helium would
be 1s2 lithium would be 1s2 2s1
beryllium would be 1s2 2s2 boron would
be 1s2 2s2 2p1 and carbon would be 1s2
2s2 2p2 now you might be wondering how
to keep track of what order in which to
fill these orbitals here's a simple
diagram you could make remembering that
the N equals 1 shell contains only an S
sub shell while the N equals 2 shell
contains only s and P sub shells and
then the N equals 3 sub shell contains
only s P and D sub shells and then
finally when you get to the N equals 4
shell it contains s P D and F sub shells
so you can draw this diagram just like
this and then draw diagonal lines
through which will tell you the order in
which to fill these orbitals first you
fill
one s orbital then the two s then the 2p
orbital and then the three s and this
next step is where it gets a little bit
confusing after you fill the 3 s orbital
you fill the 3p orbital but before you
fill the 3d orbital you actually fill
the 4s orbital first and that's because
even though 4 is a higher energy level
the 4s orbital actually has a lower
energy than the 3d orbitals do so you
fill 3p and then 4 s followed by 3 D
then 4 P then 5 s etc etc etc and so
this is a great diagram to help you keep
track of which order to fill the
orbitals in because it does get a little
confusing let's look at a more
complicated example let's write out the
electron configuration for the element
argon now remember that a neutral argon
atom has 18 protons by looking at the
atomic number on the periodic table and
if it's a neutral atom that must also
mean it has the same number of electrons
or 18 electrons we then need to diagram
these 18 electrons into the proper
configuration we start with the 1s
orbital and place one two electrons with
opposite spins the next orbital we fill
is the 2's orbital where we place one
two more electrons with opposite spins
so now we've placed four electrons the
next orbitals we fill are the 2p
orbitals placing one electrons singly in
each orbital before pairing them up so
there's our fifth sixth seventh
electrons followed by the eighth ninth
tenth electrons after we fill the 2p
orbital we fill the 3s orbital and here
our eleventh and twelfth electrons after
we fill the 3s orbital we filled the 3p
orbitals and here our 13th 14th 15th
16th 17th and 18th electrons so now that
I've diagrammed all 18 electrons I know
that this is the electron configuration
for argon and if I were to abbreviate it
it would be 1s2 2s2 2p6 3s2 3p6 now
what's interesting about the noble gases
is that they have completely filled
shells and so we often use them to
abbreviate the electron configurations
of other elements so if we were to write
the electron configuration for vanadium
vanadium has 23 electrons I'm going to
write this electron configuration
directly in the abbreviated method so in
the 1s orbital I placed two electrons so
1s 2 then 2 s 2 that's 4 electrons
followed by the 2p orbitals which can
hold 6 total electrons so now I've
placed 10 electrons followed by 3 s 2
there's 12 electrons and 3 P 6
there's 18 electrons and then the 4 s 2
orbital that's 20 electrons and the last
3 electrons go into the 3 D orbital so I
have 3 D 3 this electron configuration
contains
all 23 electrons and follows the diagram
that I showed you before for remembering
which order to fill the orbitals in from
the previous slide I've drawn our
electron configuration for argon so you
can see that the electron configuration
for argon is exactly the same as the
first part of the electron configuration
for vanadium often times to write
electron configurations abbreviating the
inner shell electrons with the noble gas
configuration so I would write the
electron configuration for vanadium as
an argon core followed by 4s 2 3 D 3
thank you for watching the chemistry
solution we hope you enjoyed this
tutorial
you
