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

Answer: (B)

$r_n=\frac{n^2{a}_o}{Z},\therefore r_o\propto n_2$
$\frac{r_3}{r_1}=\frac{9}{1}$
$r_3=9r_1=9x$
Also $mv{r}_n=\frac{nh}{2\pi }$
$mv{r}_3=\frac{3h}{2\pi }$
$mv=\frac{h}{6\pi x}$
$\lambda =\frac{h}{mv}=6\pi x$