Question

In the Bohr model, an electron of a hydrogen atom moves in a circular orbit of radius 5.3 × 10^–11 m at a speed of 2.2 × 10⁶ m/s, then the current in the orbit will be
1. 2.20 mA
2. 5.30 mA
3. 8.00 mA
4. 1.06 mA

Answer 1

Correct Answer - Option 4 : 1.06 mA

Concept:

Current is defined as rate of flow of charge.

I = q / t

Calculation:

Charge q = charge on electron = 1.602 × 10⁻¹⁹ C

radius of path = 5.3 × 10–11 m 

Circumferance = 2 π r = 2 π (5.3 × 10–11 m )

speed = 2.2 × 106 m/s

Speed = distance / time

distance here is circumferance 

\(time = \frac{distance}{speed}\)

\(\implies time \ t = \frac{2 \pi × 5.3 × 10 ^{-11} }{2.2 × 10 ^6 } = 15.13 ×10 ^{-17} \)

Current = q / t

\(\implies i = \frac{1.602 × 10 ^{-19}}{15.136 × 10 ^{-17}}\)

i = 1.06 × 10 ^-1 A  = 106 m A