Which of the following is a correct set of quantum numbers for an electron in a 5f orbital and explain why
a)n=5, l=3, ml=+1
b)n=4, l=3, ml=0
c)n=4, l=2, ml=+1
d)n=5, l=4, ml=3

The correct set of quantum numbers for an electron in a 5f orbital is n =5, l=3, ml=+1.

Electrons in orbitals can be described by four sets of quantum numbers which are;

The principal quantum(n) number takes on positive integer values from 1 to infinity. The orbital quantum number (l) takes on values from 0 to (n - 1). The magnetic quantum number takes on values ranging from -l to +l. The spin quantum number takes on values of ±1/2.

Given these restrictions and knowing that s p d f corresponds to 0 1 2 3, it follows that, the correct set of quantum numbers for an electron in a 5f orbital is n =5, l=3, ml=+1.

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Explanation:

1) n is the main or principal quantum number. It is an integer number from 1. So, it may be 1, 2, 3, 4, 5, ...

2) In 5f, the principal quantum number is n = 5.

So, the possible correct choices are A) n = 5, ℓ = 3, mℓ = +1 or D) n = 5, ℓ = 4, mℓ = 3.

3) ℓ is the second or the orbital angular momentum quantum number.

ℓ can be an integer number from 0 to n - 1.

So, when n = 5, ℓ can be 0, 1, 2, 3 or 4, only one of those.

This quantum number is also the subshell or kind of orbital.

This summarizes the relation between the number and the letter that identifies the kind of orbital:

    ℓ             kind of orbital

   0                     s

    1                     p

    2                    d

    3                     f

So, for an electron in 5f orbital, the first two quantum numbers are n = 5, ℓ = 3.

With that, you already know that the correct choice can only be A) n = 5, ℓ = 3, mℓ = +1.

4) mℓ is the third or the magnetic quantum number. This quantum number can take the values from - ℓ to + ℓ. So, for ℓ = 3 (or f) , it can be -3, -2, -1, 0, +1, +2,  or +3.

Hence, A) n = 5, ℓ= 3, mℓ= +1 is a correct set of quantum numbers for an electron in a 5f orbital.