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  • Monochromatic radiation of wavelength is incident on a hydrogen sample in its ground state. Hydrogen atom absorb. The eight and subsequently emit

Monochromatic radiation of wavelength \lambda is incident on a hydrogen sample in its ground state. Hydrogen atom absorb. The eight and subsequently emit radiation of ten different wavelength. The value of \lambda is

Option: 1

95\, \mathrm{nm}


Option: 2

103 \mathrm{~nm}


Option: 3

73 \mathrm{~nm}


Option: 4

88 \mathrm{~nm}


Answers (1)

\text{Number of wavelength is }\mathrm{\frac{n(n+1)}{2}=10}
\mathrm{\Rightarrow n^2+n-20=0}
\mathrm{\Rightarrow n=5 \quad \frac{1}{\lambda}=R\left(\frac{1}{12}-\frac{1}{52}\right)=R\left(1-\frac{1}{25}\right)-\frac{24 R}{25}}
\mathrm{\lambda=\frac{25}{24}\left(\frac{1}{R}\right)=\frac{25}{24} \times 91.2 \mathrm{~nm}=95 \mathrm{~nm}}

Posted by

Ramraj Saini

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