Introduction:
In a hydrogen atom, the electron revolves around the nucleus in a circular orbit. This orbital motion of the electron creates a magnetic moment. The magnetic moment is a measure of the strength and orientation of the magnetic field created by a current loop.

Magnetic Moment:
The magnetic moment associated with the orbital motion of the electron can be calculated using the formula:
μ = IA
where μ is the magnetic moment, I is the current, and A is the area of the current loop.

Current:
The current is given by the equation:
I = nev
where I is the current, n is the number of revolutions per second, e is the charge of the electron, and v is the velocity of the electron.

Velocity:
The velocity of the electron can be calculated using the formula:
v = (2πr)/T
where v is the velocity, r is the radius of the orbit, and T is the time taken for one revolution.

Time Taken for One Revolution:
The time taken for one revolution can be calculated using the formula:
T = 1/n
where T is the time taken for one revolution and n is the number of revolutions per second.

Substituting the Equations:
Substituting the equations for velocity and time taken for one revolution into the equation for current, we get:
I = ne(2πr)/(1/n)
Simplifying the expression, we get:
I = 2πn^2er

Area of the Current Loop:
The area of the current loop is given by the equation:
A = πr^2

Substituting the Equations:
Substituting the equation for the area of the current loop into the equation for magnetic moment, we get:
μ = IA
μ = (2πn^2er)(πr^2)
μ = 2π^2n^2er^3

Conclusion:
The magnetic moment associated with the orbital motion of the electron in a hydrogen atom is given by the equation μ = 2π^2n^2er^3, where μ is the magnetic moment, n is the number of revolutions per second, e is the charge of the electron, and r is the radius of the orbit.