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
B
450 nm
C
350 nm
D
525 nm

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 nm1 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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