JEE Main Maths: Structure of Atom questions with solutions

Q1. For an electron in an atom, the quantum numbers satisfy n + l = 5 and |mₗ| = 1. Which of the following statements is correct?

1. Number of possible orbitals satisfying these conditions is 4
2. Maximum number of electrons with mₛ = +1/2 satisfying these conditions in an atom is 6
3. For iron (Z = 26), the number of electrons satisfying these conditions is 1 only
4. None of the above

Answer: Number of possible orbitals satisfying these conditions is 4

The valid (n, l) pairs are (4,1) and (3,2), each contributing 2 orbitals (mₗ = +1 and -1), giving 4 orbitals total. Each can hold 1 electron with mₛ = +1/2, so max electrons with mₛ = +1/2 is 4 (not 6). For Fe ([Ar] 3d⁶ 4s²), the 3d orbitals with mₗ = ±1 each hold one electron from the first 5 fills, giving 2 electrons satisfying the condition (not 1). Hence only statement A is correct.