Question

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

• A. $J_n\alpha {\lambda }_n$
• B. ${\lambda }_n\infty \frac{1}{J_n}$
• C. ${\lambda }_n\infty J_n^2$
• D. none of these

Answer 1

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

$J=\frac{nh}{2\pi }=mvr$
$J=mvr,\lambda =\frac{h}{mv}$
$v\alpha \frac{1}{n},r\alpha n^2$
$\Rightarrow \lambda \alpha n$
$J\alpha n$
$\Rightarrow J\alpha \lambda$