Question

If de-Broglie wavelength of an electron in the nth Bohr orbit is ${\lambda }_n$ and angular momentum is $J_n$, then

• A. ${\lambda }_n\propto J_n$
• B. ${\lambda }_n\propto \frac{1}{J_n}$
• C. ${\lambda }_n\propto J_n^2$
• D. ${\lambda }_n\propto \sqrt{J_n}$

Answer 1

The correct option is A ${\lambda }_n\propto J_n$

${\lambda }_n=\frac{h}{P_n}=\frac{h}{m{v}_n}$
$J_n=\frac{nh}{2\pi }$
We know $V_n\propto \frac{1}{n}$ i.e., ${\lambda }_n\propto n$ and $J_n\propto n$
So ${\lambda }_n\propto J_n$