Question

Problem page an electron in an atom is known to be in a state with magnetic quantum number =ml−2 . what is the smallest possible value of the principal quantum number n of the state?

Answer 1

n = 3. The principal quantum number must be at least 3 to have a magnetic quantum number ml = -2

The rules are:

• n > 0

• l < n

• |ml| ≤ l

Thus, if ml = -2, l ≥ 2.

If l ≥ 2 and n > l, the allowed values of n are 3, 4, 5, etc.

The smallest allowed value of n is n  = 3.

Answer 2

The smallest possible value of the principal quantum number n of the state is n = 3

The four sets of quantum numbers that describe the position of an electron in an atom are;

• Principal quantum number (n) whose values range from 1 to infinity
• Orbital quantum number (l) whose values range from 0 to (n - 1)
• Magnetic quantum number(ml) whose value ranges from -l to +l
• Spin quantum number(ms) whose value is ±1/2.

For an atom having magnetic quantum number ml = -2, the smallest possible value of the  principal quantum number n of the state is n= 3 because a magnetic quantum number ml = -2 corresponds to a d orbital.

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