Which one of the following set

Which one of the following sets of quantum numbers could bethose 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 ANSWERAND HOW YOU GET TO THESE ANSWERS. I DONT GET WHY!

Answer:

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

Now, let us define the quantum numbers:

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

l =  Orbital Angular Momentum Quantum Number. Thisdetermines the “shape” of the orbital. This then makes the angulardistribution. Typical values depend directly on “n” value. then l =n-1 always. Note that these must be then positive integers, avoidfractions, decimals. Since n can be 1, then l = 1-1 = 0 can have azero value.

ml = Magnetic Quantum Number. States the orientation of theelectron within the subshell. Therefore, it also depends directlyon the “l” value. Note that orientation can be negative as well,the formula:

ml = +/- l values, therefore, 0,+/-1,+/- 2,+/-3 … Avoidfractions and decimals

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

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 isconsidered 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 cantassume

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 betrue


 
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