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Atoms — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAtoms2 Marks
Question
Using Bohr’s postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr’s radius.
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Answer

For the electron, we have
Bohr’s Postulate $(\text{mvr} = \frac{\text{nh}}{2\pi})$
$\frac{\text{mv}^{2}}{\text{r}} = \frac{1}{4\pi\in_{o}}\frac{\text{ze}^{2}}{\text{r}^{2}}$
and mvr $ = \frac{\text{nh}}{2\pi}$
$\therefore\text{m}^{2}\text{v}^{2}\text{r}^{2} = \frac{\text{n}^{2}\text{h}^{2}}{4\pi^{2}}$
and $mv^2r = \frac{1}{4\pi\in_{o}}\text{ze}^{2}$
$\therefore\text{r} = \frac{\in_{o}\text{n}^{2}\text{h}^{2}}{\pi\text{ze}^{2}\text{m}}$
Bohr’s radius (for n = 1) = $\in_{o } \text{h}^{2}/\pi\text{ze}^{2}\text{m}.$

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