What is the maximum number of electrons in an atom that can have the following quantum numbers? a. n = 3, m1 = -2;
b. n = 4, l = 3;
c. n = 5, l = 3, ml = 2;
d. n = 4, l = 1 ml = 0.

Explanation:

a ) n = 3, m1 = -2

when n = 3 , l = 0 , 1 , 2 .

when l = 2 , one electron may have m = -2 .

two electrons with s = + 1/2 and - 1/2 may have m = -2 .

So only two electrons may have the configuration of n = 3 , m = -2 .

b )  n = 4, l = 3

when , n = 4 and l = 3 , m may have values -3 , -2 , -1 , 0 , 1 , 2 , 3 . Each m have two electrons with s = + 1/2 and - 1/2 .

So altogether there are 7 x 2 = 14 electrons that have configuration of n = 4, l = 3 .

c ) n = 5, l = 3, ml = 2

Similar to case of a ) , only two electrons with s = + 1/2 and - 1/2 may have configuration of n = 5, l = 3, ml = 2

d ) n = 4, l = 1 ml = 0.

In this case also only two electrons may have configuration of

n = 4, l = 1 ml = 0. with s = + 1/2 and - 1/2 .