JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Modern Physics

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Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its(i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

(A) $3 : 4$ ✓ Correct
(B) $4 : 3$
(C) $1 : 4$
(D) $4 : 1$

Answer: (A)

Solution

The energy of the nth level is

E_{n} = \frac{- 13.6}{n ^{2}} eV

. For transition from

n = 2

n = 1

Δ E_{1} = E_{2} - E_{1} = 13.6 (1 - \frac{1}{4}) = 13.6 \times \frac{3}{4}

. For transition from

n = \infty

n = 1

Δ E_{2} = E_{\infty} - E_{1} = 13.6

. The ratio is

\frac{Δ E _{1}}{Δ E _{2}} = \frac{3}{4}

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option

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