Question

If the radius of first Bohr orbit is $x$, then de Broglie wavelength of an electron in $4^{th}$ orbit is nearly:

• A. $6\pi x$
• B. $16\pi x$
• C. $8\pi x$
• D. None of these

Answer 1

Answer: (A)

$6\pi x$

$r_n=n^2{r}_1$

For, $r_3=9r_1=9x$

Therefore, $mvr=\frac{h}{2\pi }$

$⟹mv9x=3\frac{h}{2\pi }$

Hence $mv=6\pi x$

$\lambda =6\pi x$

Hence, the correct option is $\text{A}$