In a hydrogen atom, an electron moves in an orbit of radius $5 × 10^{-11} m$ with a speed of $2.2 × 10^6 m/s$. The equivalent current is
Answer & explanation
Correct answer: option 1
The correct answer is Option (3) → $1.12 × 10^{-3} A$
Charge of electron $e = 1.6 \times 10^{-19} \, C$
Radius of orbit $r = 5 \times 10^{-11} \, m$
Speed $v = 2.2 \times 10^{6} \, m/s$
Time period of revolution: $T = \frac{2 \pi r}{v}$
$T = \frac{2 \pi (5 \times 10^{-11})}{2.2 \times 10^{6}}$
$T = \frac{3.14 \times 10^{-10}}{2.2 \times 10^{6}}$
$T \approx 1.43 \times 10^{-16} \, s$
Equivalent current: $I = \frac{e}{T}$
$I = \frac{1.6 \times 10^{-19}}{1.43 \times 10^{-16}}$
$I \approx 1.12 \times 10^{-3} \, A$
Final Answer: $1.1 \, mA$