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 $=\frac{k{Z}^2{e}^2}{2n^2}$
ie, $k\propto \frac{1}{n^2}$ and linear momentum is proportional to $1/n$.