Question

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

• A. $\frac{e^{12}}{2C{ϵ}^h}$
• B. $\frac{e^2}{2C{ϵ}^h}$
• C. $\frac{e^3}{2C{ϵ}^h}$
• D. $\frac{e^4}{2C{ϵ}^h}$

Answer 1

The correct option is B $\frac{e^2}{2C{ϵ}^h}$

reed of an electron in $n^{th}$ orbit (for Hydrogen- like system) is given by :

$v=\frac{KZ{l}^2}{nh}[whereK:\frac{1}{4\pi {ϵ}_0}\times h=\frac{h}{2\pi }]$

For first orbit of Hydrogen, $n=1kz=1$

$\Rightarrow v_1=\frac{2\pi e^2}{4\pi {ϵ}_{0}h}=\frac{e^2}{2{ϵ}_{0}h}.$

Now, velocity of speed, $=c$, so Ratio :

$\Rightarrow \frac{v_1}{c}=\frac{e^2}{2c{ϵ}_{0}h}.$