Question

In Bohr's atomic model, speed and time period of revolution of an electron in $n=3$ level are respectively

• A. $v=1.09 \times 10^{6} ms ^{-1}, T=1.52 \times 10^{-16} s$
• B. $v=2.19 \times 10^{6} ms ^{-1}, T=1.52 \times 10^{-16} s$
• C. $v=7.29 \times 10^{6} ms ^{-1}, T=1.22 \times 10^{-16} s$
• D. $v=7.29 \times 10^{5} ms ^{-1}, T=4.10 \times 10^{-15} s$

Answer 1

Answer: (D)

Using, $v_{n}=\frac{1}{137} \frac{c}{n}$,
we get $v_{3}=\frac{1}{137} \times \frac{3 \times 10^{8}}{3}$
$=7.29 \times 10^{5} ms ^{-1}$
Also, $T_{n}=\frac{2 \pi r}{v}$
$\therefore T_{3}=\frac{2 \pi r_{3}}{v_{3}}=\frac{2 \pi\left(3^{2} \times 0.53 \times 10^{-10}\right)}{7.29 \times 10^{5}}$
$=4.10 \times 10^{-15} s$