Question

Number of waves made by Bohr electron in one complete revolution in its fourth orbit is:

• A. 2
• B. 3
• C. 4
• D. $\infty$

Answer 1

Answer: (C)

4

Radius of fourth orbit $=\mathrm{0.529.}\frac{4^2}{1^2}\mathring{A}$

$=8.464R$

The velocity of electron in fourth orbit

$V_4=2.16\times {10}^6\times \frac{1}{4}m/s$

$=5.4\times {10}^{5}m/s$

$\lambda =\frac{nh}{mv}$

$n=\frac{\lambda mv}{h}$

$=\frac{2\pi r_{n}m{v}_n}{h}$

$=\frac{2\times 3.14\times 8.464\times {10}^{-10}\times 9.1\times {10}^{-31}\times 5.4\times {10}^5}{6.626\times {10}^{-34}}$

$=3.94$

$\simeq 4$

Hence, the correct option is $\text{C}$