First slide

Bohr's atom model

Question

A hydrogen-like atom emits radiations of frequency $2.7 \times 10^{15} Hz$ when it makes a transition from n = 2 to n = 1. The frequency emitted in a transition from n = 3 to n = 1 will be

Moderate

A

$1.8 \times 10^{15} Hz$
B

$3.2 \times 10^{15} Hz$
C

$4.7 \times 10^{5} Hz$
D

$6.9 \times 10^{15} Hz$

Solution

$f = c Z^{2} R [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] \Rightarrow 2.7 \times 10^{15} = c Z^{2} R [\frac{1}{1^{2}} - \frac{1}{2^{2}}] f^{'} = c Z^{2} R [\frac{1}{1^{2}} - \frac{1}{3^{2}}] Divide and solve to get: f = 3.2 \times 10^{15} Hz$

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