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The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 \mathrm{~nm}. The smallest wavelength in the infrared region of the hydrogen spectrum is -
 

Option: 1

802 \mathrm{~nm}


Option: 2

823 \mathrm{~nm}


Option: 3

1882 \mathrm{~nm}


Option: 4

1648 \mathrm{~nm}


Answers (1)

best_answer

The series is U-U region is Lyman series. longest wavelength corresponding to minimum energy which occurs in transition from

\begin{aligned} & \mathrm{n=2 \text { to } n=1} \\ &\mathrm{ 122=\frac{1 / R}{\left(\frac{1}{1^2}-\frac{1}{2^2}\right)} \quad \quad \dots(1)}\\ & \end{aligned}

The smallest wave length in the infrared region corresponds to maximum energy of paschen series.

\mathrm{\lambda=\frac{1 / R}{\left(\frac{1}{3^2}-\frac{1}{\infty}\right)} \quad \quad \dots(2)}

Divide (1) & (2)

\begin{aligned} \frac{122}{\lambda} & =\mathrm{\frac{1 / R}{\left(1-\frac{1}{4}\right)} \times \frac{\frac{1}{9}}{1 / R}=\frac{1}{9} \times \frac{4}{3} }\\ \lambda & =823.5 \mathrm{~nm} \end{aligned}
 

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Riya

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