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Monochromatic radiation of wavelength la...

Monochromatic radiation of wavelength `lambda` is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiations of six different wavelength . Find the wavelength `lambda`.

A

97.5 nm

B

12.75 nm

C

14.42 `overset(@)(A)`

D

0.85 nm

Text Solution

Verified by Experts

The correct Answer is:
A
As the hydrogen atoms emit radiation of six different wavelengths, some of them must have been excited to n = 4. The energy in n = 4 state is,
`" "E_(4)=E_(1)/4^(2)=-(13.6eV)/16=-0.85eV`
The energy needed to take a hydrogen atom from its ground state to n = 4 is,
`13.6 eV-0.85 eV=12.75eV`
The photons of the incident raditation should have 12.75 eV of energy. So,
`" "(hc)/lambda=12.75 eV`
or `lambda=(hc)/(12.75 eV)=(1242" "eV" "nm)/(12.75" "eV)=97.5 nm`
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