A monochromatic beam of light is absorbed by a collector of ground state hydrogen atom in such a way that six different wavelengths are observed when hydrogen relaxes back to the ground state. The wavelength of the incident beam is

Options

A. 92
B. 97
C. 88
D. 51

Answer

B

Explanation

Since the emitted radiation contains six different types of wavelengths , n=4
Energy of hydrogen atom for n=4 is `E=E_1/n^2=(-13.6)/16`=-0.85 eV
energy of photons of incident light will be 13.6-0.850=13.75 eV
`therefore` wavelength of light incident will be
`(hc)/lambda_0=12.75xx1.6xx10^(-19)`
`rArr lambda_0=(6.63xx10^(-34)xx3xx10^8)/(12.75xx1.6xx10^(-19))`
`rArr lambda_0=0.97xx10^(-7)` =97 nm