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Q.

A photon of wavelength λ0=1615R (R is Rydberg's constant) is emitted from a hydrogen atom when its electron return to ground state from certain exited state. In place of emitting one photon, the electron could come back to ground state by

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a

emitting 3 photons of wavelengths λ1,λ2 and λ3 such that 1λ1+1λ2+1λ3=15R16

b

emitting 3 photons of wavelengths λ1 and λ2 such that 1λ1+1λ2=15R8

c

emitting 2 photons of wavelength λ1 and λ2 such that λ1+λ2=1615R

d

emitting 2 photons of wavelength λ1,λ2 and λ3 such that λ1+λ2+λ3=1615R

answer is A.

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Detailed Solution

According to Rydberg equation1λ=R112−1n2⇒11615R=R112−1n2⇒n=4So the electron can come back to ground state from n = 4 by emitting 3 photons of wavelengths λ1,λ2 and λ3
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