Question

According to Bohrs theory of hydrogen atom, for the electron in the $n^{\text {th }}$ allowed orbit the
(i) linear momentum is proportional to $1 / n$
(ii) radius is proportional to $n$
(iii) kinetic energy is proportional to $1 / n^2$
(iv) angular momentum is proportional to $n$ Choose the correct option from the codes given below:

• A. (i), (iii), (iv)
• B. (i)
• C. (i), (ii)
• D. (iii)

Answer 1

Answer: (A)

According to Bohrs theory of hydrogen atom, angular momentum is quantized
ie, $L=m v_{n} r_{n}=n\left(\frac{h}{2 \pi}\right)$
or $L \propto n$ Radius of the orbit $r_{n} \propto \frac{n^{2}}{Z}$
Kinetic energy $=\frac{k Z^{2} e^{2}}{2 n^{2}}$
ie, $k \propto \frac{1}{n^{2}}$ and linear momentum is proportional to $1 / n$.