In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Aᵒ. If the speed of electron is 2.2 × 10⁶ m/s, then the current associated with the electron will be _____________ × 10⁻² mA. [Take π as 22/7]

Solution

Physics sir · 4 steps

The electron passes any point on its orbit f times a second, so the current is just e times f.

1. Current from motion. Current is the charge passing a point per second. The electron carries charge e past a point once per revolution, so I = e f, where f is the number of revolutions per second.

   I = e f = (e v)/(2π r)

2. Find the frequency. The orbit length is 2π r = 2 × 22/7 × 0.5 × 10⁻¹⁰ = 22/7 × 10⁻¹⁰ m. So f = (2.2 × 10⁶ × 7)/(22 × 10⁻¹⁰) = 7 × 10¹⁵ s⁻¹.
3. Put in charge. I = 1.6 × 10⁻¹⁹ × 7 × 10¹⁵ = 1.12 × 10⁻³ A = 1.12 mA.
4. So. 1.12 mA = 112 × 10⁻² mA, so the blank is 112.

The common slip: 1.12. Writing the current in mA as 1.12 ignores the × 10⁻² in the blank. The number to enter is 112.

The idea to keep. A charge going round in a circle acts like a current loop: I = q/T = qv/(2π r). Convert the radius to metres first, then match the units the blank asks for.

Answer from the NTA final answer key. Solution by PrepWiser.