Q156 / 160 · TS EAMCET 2021 (05 Aug Shift 2) · Physics

A hydrogen atom emits a photon corresponding to an electron transition from $n = 5$ to $n = 1 .$ If $R$ is the Rydberg constant, then the wavelength of emitted photon is

Correct answer
A
$\frac{25}{24 R}$
B
$\frac{24 R}{25}$
C
$\frac{4}{5 R}$
D
$\frac{5 R}{4}$

Solution

From Rydberg's equation, wavelength is related to transition is given by,

\frac{1}{λ} = R (\frac{1}{{n_{f}}^{2}} - \frac{1}{{n_{i}}^{2}})

\Rightarrow \frac{1}{λ} = R (\frac{1}{1^{2}} - \frac{1}{5^{2}})

\Rightarrow \frac{1}{λ} = R (\frac{25 - 1}{25})

\Rightarrow \frac{1}{λ} = (\frac{24 R}{25})

\Rightarrow λ = (\frac{25}{24 R})

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

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