Question

If $r_0$ be the radius of first Bohr's orbit of $H-$atom, then the de-Broglie's wavelength of an electron revolving in the third Bohr's orbit will be:

• A. $2\pi r_0$
• B. $4\pi r_0$
• C. $6\pi r_0$
• D. $\pi r_0$

Answer 1

The correct option is C $6\pi r_0$

$mvr=nh/2\pi$ ---(1)

$p=\frac{h}{\lambda }=mv$ --(2)

Placing the value of $mv$ from Eq. (2) into Eq. (1) for 3rd orbit

$\frac{h{r}_3}{\lambda }=3h/2\pi$

$\lambda =2\pi \frac{r_3}{3}$

$r_3=n^2{r}_0=9r_0$

So $\lambda =2\pi \times 9r_0/3=6\pi r_0$

Option C is correct.