A hydrogen atom is in an excited state of principal quantum number ( n ) , it emits a photon of wavelength ( λ ) , when it returns to the ground state. The value of n is

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As λ 1 ​ = R ( n 1 2 ​ 1 ​ − n 2 2 ​ 1 ​ ) ∴ λ 1 ​ = R ( 1 2 1 ​ − n 2 1 ​ ) Multiply both sides by λ 1 = λ R ( 1 − n 2 1 ​ ) or λ R 1 ​ = 1 − n 2 1 ​ or n 2 1 ​ = 1 − λ R 1 ​ = λ R λ R − 1 ​ or n = λ R − 1 λ R ​ ​

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