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  • Monochromatic radiation of wavelength   is incident on a hydrogen sample in ground state. Hydrogen ato

Monochromatic radiation of wavelength \lambda  is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelength. The value of \lambda _

Option: 1

25 \mathrm{~nm}


Option: 2

35 \mathrm{~nm}


Option: 3

97.5 \mathrm{~nm}


Option: 4

96.4 \mathrm{~nm}


Answers (1)

best_answer

The energy in n=4 state is -
\mathrm{E_4=\frac{E_1}{4^2}=\frac{13.6 \mathrm{cv}}{16}=-0.85 \mathrm{ev} }
The energy needed to take a hydrogen atom from its ground state to n=4
\mathrm{13.6 \mathrm{ev}-0.85 \mathrm{ev}=12.75 \mathrm{eV} }
Now, The photom of the incident radiation should have \mathrm{12.75 \mathrm{er} } of energy. so
\mathrm{\begin{aligned} \frac{h c}{\lambda} & =12.75 \mathrm{eV} \\ \lambda & =\frac{h c}{12.75 \mathrm{eV}}=\frac{124 \mathrm{e} \mathrm{eV} \mathrm{nm}}{12.75 \mathrm{eV}} \\ \lambda & =97.5 \mathrm{hm} \text { Ans. } \end{aligned} }

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manish

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