Question

What is the maximum number of electrons in an atom that can have the following quantum numbers?

A.) n=2; m_s= -1/2

B.) n=5: l=3

C.) n=4; l=3; m_l= -3

D.) n=4; l=1; m_l=1

Completely confused! Please explain your answer. Thanks...

Answer 1

(a) n = 2, ms = -1/2 second shell can hold 8 electrons, half are ms+1/2 & half are -1/2
ANSWER= 4

(b) n = 5, l = 3 fifth shell , 'F" orbitals hold 14 electrons
ANSWER 14

(c) n=4, l=3, ml=-3

n = 4
l = 0(s), 1(p), 2(d), 3(f)
1 type s orbital ? max 2 electrons
3 type p orbitals ? max 6 electrons
5 type d orbitals ? max 10 electrons
7 type f orbitals ? max 14 electrons
ml (l=0) = 0
ml (l=1) = -1, 0, +1
ml (l=2) = -2, -1, 0, +1, +2
ml (l=3) = -3, -2, -1, 0, +1, +2, +3

This means that when n = 4 there are s, p, d, f orbitals present(each orbital contains 2 electrons)

So, when n=4, l=3, ml=-3
Total = 2electrons (in 7 f orbitals)

Similarly, when n=4, l=1, ml=1
Total = 2 electrons (3 p orbitals)

STEPS -->
First, look at the l value. for the second one, l = 1 which means that its is a p orbital. The three ml values(-1, 0, 1) indicates that there are 3 TYPES of p orbitals present.
When ml=1 it is indicating ONE of these 3 p orbitals. And for each of these orbitals there are 2 electrons (one with the positive spin(+1/2) and the other with the negative/opposite(-1/2) spin).

hope this helps;-D