Ratio of Magnetic Dipole Moment to Angular Momentum in Hydrogen Atom

Introduction:
The hydrogen atom has only one electron revolving around the nucleus in a circular orbit. The electron has both angular momentum and magnetic dipole moment.

Ratio of magnetic dipole moment to angular momentum:
The ratio of magnetic dipole moment to angular momentum of the electron in the first orbit of hydrogen atom is given by the formula:

μ / L = -e / 2mb

where,
μ = magnetic dipole moment
L = angular momentum
e = charge of the electron
m = mass of the electron
b = radius of the first orbit

Explanation:
The magnetic dipole moment is a measure of the strength of a magnetic field produced by a current loop. The angular momentum is the product of the mass, velocity, and radius of the orbit. In the case of the hydrogen atom, the electron revolves around the nucleus in a circular orbit. The electron has a charge and a mass, which gives rise to both the magnetic dipole moment and the angular momentum.

The negative sign in the formula indicates that the magnetic dipole moment and the angular momentum are in opposite directions. The electron in the first orbit of the hydrogen atom has the smallest radius, which means that it has the highest angular momentum and the lowest magnetic dipole moment.

Conclusion:
In conclusion, the ratio of magnetic dipole moment to angular momentum of the electron in the first orbit of hydrogen atom is -e / 2mb. This ratio is important in understanding the behavior of the electron in the hydrogen atom and its interaction with external magnetic fields.