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

Q . 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

(a)     √[λR(λR-1) ]

(b) √λ(R-1)/λR

(c) √ [λR/(λR-1) ]

(d) √λ(R-1)

Ans: (c)

Sol: 1/λ = R[1/1² – 1/n²]

1/λR  = 1- 1/n²

1/n² = 1- 1/λR  =( λR – 1)/λR

n = √ [λR/(λR-1) ]