For hydrogen atom, λ 1 and λ 2 are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of λ 1 and λ 2 is 32 x . The value of x is ______.

Question

For hydrogen atom, λ 1 ​ and λ 2 ​ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of λ 1 ​ and λ 2 ​ is 32 x ​ . The value of x is ______.

TestHub · Accepted Answer

Wavelength corresponding to the photon emitted in transition $n = 3 t o n = 1$ is

$\frac{1}{λ _{1}} = R (\frac{1}{1 ^{2}} - \frac{1}{3 ^{2}}) = \frac{8 R}{9}$ ....(1)

Wavelength corresponding to the photon emitted for transition in transition $n = 2 t o n = 1$ is

$\frac{1}{λ _{2}} = R (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}) = \frac{3 R}{4}$ ....(2)

$\frac{λ _{1}}{λ _{2}} = \frac{3 R}{4} \times \frac{9}{8 R} = \frac{27}{32}$

Hence, the value of $x = 27$ .

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