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Monochromatic radiation of specific wavelength is incident on H-atoms in ground state. H-atoms absorb energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations:

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97.25nm

85.8 nm

50nm

9.75 nm

answer is D.

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Detailed Solution

H-atom emits 6 spectral lines
$\frac{n (n - 1)}{2} = 6$ ;
n=4
∴ ΔE = E₄− E₁ = $\frac{- 13.6}{{(4)}^{2}} - \frac{(- 13.6)}{{(1)}^{2}}$

= 13.6 − 0.85 = 12.75 eV

ΔE = $\frac{hc}{λ}$
λ = $\frac{hc}{∆ E}$
λ = $\frac{12.42}{12.75}$
λ = 97.25 nm

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