The electron in hydrogen atom is moving in an orbit of radius $0.53 Å$. It takes $1.571 \times 10^{-16}…

The electron in hydrogen atom is moving in an orbit of radius $0.53 Å$. It takes $1.571 \times 10^{-16} \mathrm{~s}$ to complete one revolution. The velocity of electron will be $[\pi=3 \cdot 142]$
  1. $5.3 \times 10^{6} \frac{\mathrm{m}}{\mathrm{s}}$
  2. $4 \times 10^{6} \frac{\mathrm{m}}{\mathrm{s}}$
  3. $3 \times 10^{8} \frac{\mathrm{m}}{\mathrm{s}}$
  4. $2 \cdot 12 \times 10^{6} \frac{\mathrm{m}}{\mathrm{s}}$

Solution

$r=0.53 Å, t=1.571 \times 10^{-16} \mathrm{sec}$ $v=\frac{2 \pi r}{t}=2 \times \frac{22}{7} \times \frac{53}{100} \times 10^{-10} \times \frac{10^{11}}{1.57}$ $=\frac{2 \times 22 \times 53}{700 \times 1.571 \times 10^{6}}$ $=2.12 \times 10^{6} \mathrm{~m} / \mathrm{s}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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