Question

In the Bohr model of the hydrogen atom, an electron in the 1st excited state moves at a speed of 2.19 106 m/s in a circular path having a radius of 5.29 10-11 m. What is the effective current associated with this orbiting electron?

Answer 1

Answer:

I = 1.05x10⁻³ A

Explanation:

By definition, an electric current is the rate of charge flow at a given time:

$I = \frac{q}{t}$

Where:

q: is the electrons charge = 1.602x10⁻¹⁹ C

t: is the time

In a circular motion, the time is given by:

$t = T = \frac{2\pi}{\omega} = \frac{2\pi}{v/r} = \frac{2\pi r}{v}$

Where:

ω: is the angular speed = v/r

v: is the speed = 2.19x10⁶ m/s

r: is the radius = 5.29x10⁻¹¹ m

$t = \frac{2\pi r}{v} = \frac{2\pi 5.29 \cdot 10^{-11} m}{2.19 \cdot 10^{6} m/s} = 1.52 \cdot 10^{-16} s$

Now, the effective current is:

$I = \frac{q}{t} = \frac{1.602 \cdot 10^{-19} C}{ 1.52 \cdot 10^{-16} s} = 1.05 \cdot 10^{-3} A$  

Therefore, the effective current associated with this orbiting electron is 1.05x10⁻³ A.

I hope it helps you!