Question

If the radius of first Bohr orbit is x, then de-Broglie wavelength of electron in $3^{rd}$ orbit is nearly:

• A. $2\pi x$
• B. $6\pi x$
• C. 9x
• D. $\frac{x}{3}$

Answer 1

The correct option is B

$6\pi x$

$r_n=n^2{r}_1$

So, the third radius would be $r_3=9r_1=9x$

angular momentum is given by: $mvr=h/2\pi$

$mv\left(9x\right)=3h/2\pi$

$h/mv=6\pi x$

$\lambda =6\pi x$