let's take a look at a practice problem regarding quantum
numbers and electron configurations. so the question is for a neutral atom of
arsenic first what is its ground state electron configuration and to what
quantum numbers would be assigned to the electrons in its highest energy sub
shell? so if this sounds confusing go ahead and check out my tutorial on
quantum numbers and electron configuration it's very thorough and it
will elucidate all of these concepts for you. so once all of that makes sense give
this one a try so the first thing we have to do is get the electron
configuration of arsenic so let's find arsenic there it is number 33 on the
periodic table so let's start working through the blocks of the periodic table
if we start in the first row that gives us 1 s 2 those are the electrons for
hydrogen and helium then moving to the second period we have 2s2 2p6 moving to
the third period we have 3s2 3p6 moving to the fourth period we have 4s2 then
we go through the d-block and remember that the d-block is one behind the s and
p blocks so we have three d-10 and then to get to arsenic we're moving through
the p block we have four P three because it's the third element through the P
block so that will be the ground state electron configuration for arsenic 1s2
2s2 2p6 3s2 3p6 4s2 3d10 4p3 we can abbreviate that with
arghh encore if we like which would be followed by 4s2 3d10 4p3 so now to talk
about quantum numbers let's get rid of the periodic table we want to know the
quantum numbers associated with the electrons in the highest energy sub
shell. now remember according to the aufbau principle these orbitals are
filled in this order because they are increasing in energy each next sub shell
is higher in energy than the previous so the highest energy sub shell is the 4p
sub shell so let's draw out the 4p orbitals and those are going to look
like this so there are 3p orbitals for each energy level and if we have 4 P 3
we have 3 electrons that we need to put in them remember that hund's rule tells
us that we're gonna put one in each orbital before doubling any of them up
so the three four p orbitals each have one electron and they will all be
aligned in spin there will all be spin up so now that we have that let's go
ahead and assign all of our quantum numbers the first quantum number is the
principal quantum number n that corresponds to the energy level that
one's very easy because whatever we have 3s2 4s2 4p3 etc that first number
that is n so because these are 4 P orbitals
n must be 4 now let's look at L. L is describing the type of orbital so if we
are looking at an S orbital the L value would be 0 for P orbitals the L value is
1 for D orbitals the L value is 2 for F orbitals the L value is 3 we are looking
at P orbitals specifically for P orbitals that means the L value must be
1 for all of these electrons so that covers N and L and those will be the
same for all of these electrons now we get to a point where the remaining
quantum numbers may be different for each electron remember M sub L
goes from negative L to L so if L is one M sub L can be negative one zero or one
and those correspond to each individual orbital now each of these electrons is
sitting in a different orbital so each one will have a different M sub L value
so the first one can be M sub L equals negative 1 the second one can have an M
sub L value of zero and the third one can have an M sub L value of positive 1
lastly for M sub s that's the spin quantum number that has got to be plus
1/2 or minus 1/2 and since all of these must have their spins aligned we are
going to assign them all spin values up plus 1/2 so that is all set for the
quantum numbers all of those have an N value of 4 they all have an L value of 1
they each have their own M sub L value and then they all have M sub s values of plus 1/2.