An electron in a hydrogen atom is revolving around the proton in a orbit of radius r and velocity v
.find the current.
To find the current of the electron in a hydrogen atom, we need to calculate the charge per unit time passing through a given point.
The current, denoted by I, is defined as the rate of flow of charge, given by the equation:
I = ΔQ / Δt
where:
- ΔQ is the change in charge passing through a point
- Δt is the change in time
In this case, the electron is revolving around the proton in a circular orbit. The charge of an electron is e, which is approximately equal to -1.6 x 10^-19 coulombs.
To calculate the current, we first need to determine the time period of one complete revolution (T) of the electron in its orbit:
T = 2πr / v
where:
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the orbit
- v is the velocity of the electron
Once we have the time period, we can calculate the charge passing through a point on the orbit in one revolution:
ΔQ = e
Finally, we can calculate the current:
I = ΔQ / Δt
I = e / T
Substituting the value of T:
I = e / (2πr / v)
Simplifying further:
I = (e * v) / (2πr)
Therefore, the current of the electron in a hydrogen atom is given by (e * v) / (2πr).