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)

(i), (iii), (iv)

Answer 2

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 $1 / n$.