Question

The fig shows an energy levels for the electron in a certain atom which transition in a graph represents the emission of a Photon with most energy ?

(A) III

(B) IV

(C) I

(D) II

Answer 1

The correct option is (D) II.

Explanation:

E_n = [(– 13.6z²) / n²] eV for simplicity put + 13.6z² = constant = k.

Hence E_n = [(– k) / n²] eV

Hence E₁ = [(– k) / 1], E₂ = [(– k) / 4], E₄ = [(– k) / (16)], E₃ = [(– k) / 9]

Now    E₂ – E₁ = [(– k) / 4] + (k / 1) = (3k / 4) ........(1)

E₄ – E₂ = [(– k) / (16)] + (k / 4) = (3k / 16) .........(2)

E₄ – E₃ = [(– k) / (16)] + (k / 9) = [(7k) / (144)] ...........(3)

Hence (E₂ – E₁) > (E₄ – E₂) > (E₄ – E₃) hence photon with most energy occurs in II i.e. transition from n = 2 to n = 1.