Question

An electron in an atom is known to be in a state with magnetic quantum number ml=−1
What is the smallest possible value of the principal quantum number n of the state?

Answer 1

Explanation:

It is known that the maximum value of ml is equal to the vale of l. But the minimum value of n is as follows.

                    n = l + 1

where,     n = principle quantum number

                l = azimuthal quantum number

Values of n can be 1, 2, 3, 4 and so on. Whereas the values of l can be 0, 1, 2, 3, and so on.

Also, "m" is known as magnetic quantum number whose values can be equal to -l and +l.

So, when n = 1 then l = 0 and m = 0.

When n = 2 then l = 1 and values of m will be equal to -1, 0, +1. As it is given that the magnetic quantum number ml = -1. Hence, it is only possible when n = 2.

Thus, we can conclude that the smallest possible value of the principal quantum number n of the state is 2.

Answer 2

If an electron in an atom is known to be in a state with magnetic quantum number ml = −1, the smallest possible value for the principal quantum number is 2.

What are the quantum numbers?

Quantum numbers are a set of numbers that characterize an electron in an atom.

• Principal quantum number (n): refers to the level of energy.
• Azimuthal quantum number (l): refers to the sublevel of energy.
• Magnetic quantum number (ml): refers to the orientation of the orbital.
• Electron spin quantum number (ms): refers to the spin of the electron.

"ml" can take values going from "-l" to "+l". Thus, if ml = -1, "l" must be at least 1.

"l" takes values from 0 to n - 1. Thus, if l = 1, "n" must be at least 2.

If an electron in an atom is known to be in a state with magnetic quantum number ml = −1, the smallest possible value for the principal quantum number is 2.

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