NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #21According to Maxwell’s theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?Ans : Let v0 be the velocity of the electron moving in the ground state and `` {r}_{0}`` be the radius of the ground state.
Frequency of the revolution of electron in the circle is given by
`` f=\frac{{v}_{0}}{2\,\mathrm{\,\pi \,}{r}_{0}}``
Frequency of the radiation emitted = Frequency of the revolution of electron
∴ Frequency of the radiation emitted = `` \frac{{v}_{0}}{2\,\mathrm{\,\pi \,}{r}_{0}}``
Also, c = f`` \lambda ``
Here, c = Speed of light
`` \lambda `` = Wavelength of the radiation emitted
`` \Rightarrow `` `` \lambda =\frac{c}{f}``
`` \therefore \lambda =\frac{2\,\mathrm{\,\pi \,}{r}_{0}c}{{v}_{0}}``
`` =\frac{2\times \left(3.14\right)\times \left(53\times {10}^{-12}\right)\times (3\times {10}^{8})}{\left(2.187\times {10}^{6}\right)}``
`` =45.686\times {10}^{-12}\,\mathrm{\,m\,}=45.7\,\mathrm{\,nm\,}``
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