Magnetic Moment

R₀ = L

= L

R =

M' = m(2R) sin 30°

= m(2) × = mL =

To determine the magnetic moment of an electron in its lowest energy state according to the model described, we start with the quantization of magnetic flux. The quantization condition given is:

where is the magnetic flux through the electron's orbit, is an integer, is Planck's constant, and is the charge of the electron. For the lowest energy state, we consider . Thus:

The magnetic moment of an electron moving in a circular orbit due to a magnetic field is given by:

where is the current, is the area of the orbit, and is the speed of light. The current is given by the electron's charge divided by the period of its orbit.

The area of the orbit is related to the magnetic flux by:

Substituting from earlier:

In quantum mechanics, for the lowest energy state, the angular momentum is quantized and equals:

with , giving . The speed can be expressed as:

From , we solve for :

Combining all expressions, the magnetic moment in terms of known quantities is:

Thus, the magnetic moment of an electron in its lowest energy state is:

This matches the given option , confirming it as the correct answer.