Question

In Bohr's model of hydrogen atom,

• A. The radius of $nth$ orbit is proportional to $n^2$
• B. The total energy of electron in $n^{th}$ orbit is proportional to $n$
• C. The angular momentum of the electron in an orbit is an integral multiple of $h/2\pi$
• D. The magnitude of the potential energy of electron in any orbit is greater than its Kinetic energy

Answer 1

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

The expression of radius of n th orbit for H-atom: $r_n=\frac{n^2{h}^2}{4{\pi }^2{e}^{2}mk}$ where $k=1/4\pi {ϵ}_0$

so, $r_n\propto n^2$

The KE of electron for H-atom is $K_n=\frac{k{e}^2}{2r_n}$ or potential energy, $U_n=-\frac{k{e}^2}{r_n}$

Total energy $E=K_n+U_n=-\frac{k{e}^2}{2r_n}$ so $E\propto 1/r_n=1/n^2$

Also $|U_n|>K_n$

From Bohr's second postulate, angular momentum, $L=mvr=nh/2\pi$