First slide

Bohr's atom model

Question

The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is equal to (where e, h, and c have their usual meanings in cgs system)

Moderate

A

$2 π h c / e^{2}$
B

$e r^{2} h / 2 π c$
C

$e^{2} c / 2 π h$
D

$2 π e^{2} / h c$

Solution

$v_{n} = k \frac{2 π e^{2}}{n h}$
We know that in cgs system k=1
$∴ v_{n} = \frac{2 π e^{2}}{n h} \Rightarrow v_{1} = \frac{2 π e^{2}}{h}$
$So \frac{v_{1}}{c} = \frac{2 π e^{2}}{c h}$

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