Question

How many electrons could have the following set of quantum numbers?

(a) n =4, ℓ =3

(b) n =5, ℓ =3, mℓ =-3

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

a)

n = 4, l = 3; then

this implies

l = 0,1,2,3 --> s,p,d,f

f = 14 electrons

b)

n = 5, l = 3, ml = -3

then only ms = +1/2 and -1/2 will be able to exist

2 electrons