Question

What are the possible values of ml for an electron in the n=4 state?

a) ml = 4, 3, 2, 1, 0
b) ml = 0, ±1, ±2, ±3, ±4
c) ml = 1, 3, 5, 7, 9
d) ml = -4, -3, -2, -1, 0

Answer 1

b) ml = 0, ±1, ±2, ±3, ±4

The possible values of m_l for an electron in the n=4 state are m_l = 0, ±1, ±2, ±3, ±4, spanning across all possible angular momentum quantum numbers (l) from 0 to 3.

Step-by-step explanation:

The possible values of ml for an electron in the n=4 state can be determined on the basis of the quantum number l (the angular momentum quantum number).

For any given value of n, the possible values of l range from 0 to n-1. This means when n is 4, l can be 0, 1, 2, or 3. The magnetic quantum number, ml, depends on the value of l, and it can take on values from -l to +l, including 0.

Thus, given n=4 and consequently l=3, the values of ml would include -3, -2, -1, 0, +1, +2, and +3.

When considering values of ml for all allowable values of l, the complete set for an electron in the n=4 state would be ml = 0, ±1, ±2, ±3, ±4, since these include all possible ml for l=0 to l=3.