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Question

# A hydrogen atom is in an excited state of principle quantum number n. It emits a photon of wavelength λ when it returns to the ground state. The value of n is ( R is Rydberg constant)

A
λR(λR1)
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B
λR1λR
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C
λRλR1
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D
λ(R1)
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Solution

## The correct option is C √λRλR−1We know that, 1λ=R(1n21−1n22) ...(1) Here, n1=1 (ground state) n2=n (excited state) On substituting these values in equation (1), we get, ⇒1λ=R(112−1n2) ⇒1λ=R(1−1n2)=R(n2−1n2) ⇒n2=λR(n2−1)=λRn2−λR ⇒(λR−1)n2=λR ⇒n=√λR(λR−1) Hence, option (C) is correct.

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