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Atoms — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms2 Marks
Question
State Bohr’s quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum does it belong.
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Answer

According to Bohr's quantisation, the electrons revolve around the nucleus only in those orbits for which the angular momentum is the integral multiple of
$\frac{\text{h}}{2\pi}$
$\text{L}=\frac{\text{nh}}{2\pi}$
For Bracket series $\text{n}_2=\infty,$
$\frac{1}{\lambda}=\text{R}_\text{H}\text{Z}^2\Big\{\frac{1}{4^2}-\frac{1}{\infty}\Big\}$
$\frac{1}{\lambda}=\frac{\text{R}_\text{H}}{16}$
$\lambda=\frac{16}{\text{R}_\text{H}}=14.58\times10^{-7}\text{m}$
This wavelength belongs to the inftra-red region.

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