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Question

What is the wavelength of a photon emitted during a transition from $$n = 5$$ state to $$n = 2$$ state in the hydrogen atom?


A
434 nm
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B
450 nm
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C
350 nm
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D
525 nm
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Solution

The correct option is C $$434\ nm$$
$$\displaystyle  \dfrac {  1}{ \lambda }=R [\dfrac {  1 }{n^2_1  } - \dfrac {  1}{ n^2_2 }] $$

$$\displaystyle  \dfrac {  1}{ \lambda }=109677.6 \ cm^{-1} \times  [\dfrac {  1 }{2^2  } - \dfrac {  1}{ 5^2 }]$$

$$\displaystyle  \dfrac {  1}{ \lambda }=23032.3 \ cm^{-1} $$

$$\displaystyle \lambda = 4.34 \times 10^{-5} \ cm$$

Convert unit from cm to nm
1 cm $$\displaystyle =10^7 \ nm$$

$$\displaystyle \lambda = 4.34 \times 10^{-5} \ cm \times  \dfrac {10^7 \ nm}{ 1 \ cm}$$

$$\displaystyle \lambda = 434  \ nm$$

Physics

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