Q2 / 160 · TS EAMCET 2022 (20 Jul Shift 1) · Chemistry

The approximate ratio of the speed of light in vacuum to that of an electron in the first Bohr orbit of hydrogen atom is

  • A
    100 : 1
  • Correct answer
    B
    137 : 1
  • C
    157 : 1
  • D
    191 : 1

Solution

From Bohr's atomic model $$ \mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi} $$ or, $\quad \mathrm{v}=\frac{\mathrm{nh}}{2 \pi \mathrm{mr}}$ when $\mathrm{n}=1, \mathrm{~h}=6.626 \times 10^{-31} \mathrm{~J}-\mathrm{s}, \mathrm{m}=9.11 \times 10^{-31} \mathrm{~kg}, \mathrm{r}=$ $0.529 \times 10^{-10} \mathrm{~m}$ then $\mathrm{v}=2.18 \times 10^6 \mathrm{~m} / \mathrm{s}$ $$ \begin{aligned} & \therefore \quad \frac{\text { speed of light }(\mathrm{c}) \text { in vacuum }}{\mathrm{v}} \\ & =\frac{3 \times 10^8 \mathrm{~m} / \mathrm{s}}{2.18 \times 10^6 \mathrm{~m} / \mathrm{s}}=\frac{137}{1} \end{aligned} $$

Hence, the correct answer is option: 'B'.

Relevant Questions