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

I = 1.05x10⁻³ A

Step-by-step explanation:

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

`I = (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 = (2\pi)/(\omega) = (2\pi)/(v/r) = (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 = (2\pi r)/(v) = (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 = (q)/(t) = (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!