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Q.

If the longest wavelength in the ultraviolet region of hydrogen spectrum is $λ_{0}$ then the shortest wavelength in its infrared region is :

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a

$\frac{36}{5} λ_{0}$

b

$\frac{46}{7} λ_{0}$

c

$\frac{20}{3} λ_{0}$

d

$\frac{27}{4} λ_{0}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{h c}{λ_{0}} = - 13.6 (\frac{1}{2^{2}} - 1) U V r e g i o n \\ \frac{h c}{λ_{\min}} = - 13.6 (\frac{1}{\infty} - \frac{1}{3^{2}}) I R r e g i o n \\ λ_{\min} = \frac{\frac{3}{4} λ_{0}}{\frac{1}{9}} = \frac{27}{4} λ_{0} \end{array}$

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If the longest wavelength in the ultraviolet region of hydrogen spectrum is λ0 then the shortest wavelength in its infrared region is :