Question

If $a_o$ be the radius of the first orbit of Bohr's H-atom, the de-Broglie wavelength of an electron revolving in the second orbit will be:

• A. $6\Pi a_o$
• B. $4\Pi a_o$
• C. $2\Pi a_o$
• D. none of the above

Answer 1

Answer: (B)

$4\Pi a_o$

We know

$r_n=n^2{r}_1$

where

$r_n=$ Radius of nth Bohr orbit

$n=$ orbit

$r_1=$ Radius of first Bohr orbit

Here

$n=2\&r_1=a_0$

$r_2=4a_0$

$\Rightarrow mvr=\frac{h}{2\pi }$

$\Rightarrow mv\left(4a_0\right)=2\frac{h}{2\pi }$

$\Rightarrow \frac{h}{mv}=4\pi a+0$

$\Rightarrow \lambda =4\pi a_0$