Question

Which one of the following sets of quantum numbers could be those of the distinguishing (last) electron of Mo?

a) n = 4, l= 0, ml= 0, ms= +1/2

(b) n = 5,l= 1, ml= 9, ms= -1/2

(c) n = 4,l= 2, ml= -1, ms= +1/2

(d) n = 5,l= 2, ml= +2, ms= -1/2

(e) n = 3,l= 2, ml= 0, ms= +1/2

I KNOW THE ANSWER IS C BUT PLEASE EXPLAIN WHY THAT IS THE ANSWER AND HOW YOU GET TO THESE ANSWERS. I DONT GET WHY!

Answer 1

Recall Pauli Exclusion principle, which states that no two electrons can have the same quantum numbers. That is, each electron has a specific set of unique quantum numbers.

Now, let us define the quantum numbers:

n = principal quantum number, states the energy level of the electron. This is the principal electron shell. As n increases, the electron gets further and further away. "n" can only have positive integer numbers, such as 1,2,3,4,5,... Avoid negative integers, fractions, decimals and zero.

l =  Orbital Angular Momentum Quantum Number. This determines the "shape" of the orbital. This then makes the angular distribution. Typical values depend directly on "n" value. then l = n-1 always. Note that these must be then positive integers, avoid fractions, decimals. Since n can be 1, then l = 1-1 = 0 can have a zero value.

ml = Magnetic Quantum Number. States the orientation of the electron within the subshell. Therefore, it also depends directly on the "l" value. Note that orientation can be negative as well, the formula:

ml = +/- l values, therefore, 0,+/-1,+/- 2,+/-3 ... Avoid fractions and decimals

ms = the electron spin, note that each set can hold up to two electrons, therefore, we must state each spin (downwards/upwards). It can only have two values and does not depends on other values,

ms can cave only +1/2 or -1/2 spins. avoid all other numbers. also, avoid 0.5 or -0.5

knowing this, get Mo electorn configuration

[Kr] 5s1 4d5

then...

the last e-, will be that oof 4d5 present...

note that 4d requires more energy than 5s1 therefore 4d is considered the most energetic:

level = 4 ; n = 4

for "l" --> s,p,d,f --> 0,1,2

then choose l = 2, since we need "d"

Note that the "last" electorn, is the one marked with green

then

all have same spin,+1/2

if you notice,

a. can't be since l = 0, implies "s" level, which we cant assume

b can'0t be since, n = 5,

d can't be since,n = 5

e can'0t be since, n = 3

then

(c) n = 4,l= 2, ml= -1, ms= +1/2; must be true