If the electron in a hydrogen atom jumps from an orbit with level n_1=2 to an orbit with level n_2=1 the emitted radiation has a wavelength given by

Correct answer: (B) λ=4 / 3 R. 1/(λ)=R (1/(n_1^2)-1/(n_2^2) )=R (1/(1^2)-1/(2^2) )=(3 R)/4 ⇒ λ=4/(3 R)

Q127 / 160 · WBJEE 2009 · Physics

If the electron in a hydrogen atom jumps from an orbit with level $\mathrm{n}_1=2$ to an orbit with level $\mathrm{n}_2=1$ the emitted radiation has a wavelength given by

A
$\lambda=5 / 3 \mathrm{R}$
Correct answer
B
$\lambda=4 / 3 \mathrm{R}$
C
$\lambda=\mathrm{R} / 4$
D
$\lambda=3 \mathrm{R} / 4$

Solution

$\frac{1}{\lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=R\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3 R}{4}$ $\Rightarrow \lambda=\frac{4}{3 R}$

Hence, the correct answer is option: 'B'.

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