Question

According to Bohr's theory of hydrogen-atom, for the electron in the $n^{th}$ permissible orbit

• A. $\text{Linear Momentum}\propto \frac{1}{n}$
• B. $\text{Radius of orbit}\propto n$
• C. $\text{Kinetic Energy}\propto \frac{1}{n^2}$
• D. $\text{Angular Momentum}\propto n$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $\text{Linear Momentum}\propto \frac{1}{n}$
C $\text{Kinetic Energy}\propto \frac{1}{n^2}$
D $\text{Angular Momentum}\propto n$

Angular Momentum Quantisation:
$mvr=\frac{nh}{2\pi }$ ------------(1)

Centripetal force:
$\frac{k\left(e\right)e}{r^2}=\frac{m{v}^2}{r}$ ----------------(2)
$v^{2}r=\frac{k{e}^2}{m}$

Substituting (1) in (2)
$v=\frac{2\pi k{e}^2}{nh}$
Energy: $E=13.6\frac{Z^2}{n^2}$ -----------(3)
Linear Momentum:
$mvr=nh/2\pi$
$mv=\frac{nh}{2\pi r}$ ---------------(4)

From the concept attached:
$r\propto n^2$ -----------------(5)

Hence, $mv\propto \frac{1}{n}$ by (6)
and
$U=2KE$
$E\propto \frac{1}{n^2}$ (concept attached)