a) What is the magnitude of the square of the intrinsic spin angular momentum, S², of the electron in units of (h/2p)².

S² = (h/2p)².

b) How many values can the spin magnetic quantum number, m_s, have?

values.

The electron's spin angular momentum creates a spin magnetic moment. The two vectors are related by

Suppose that a free electron is in a uniform magnetic field in the z direction of T and that the electron has the largest possible value of m_s.

c) What is the z component of its magnetic moment in units of the Bohr magneton, m_B. (Be careful with +- signs.)

m_z = m_B

d) What is the magnetic potential energy, U, of the electron in this magnetic field in eV? (Note the sign.)

U = eV.

Suppose that the electron makes a transition to a state which differs in the spin magnetic quantum number, m_s, by one.

e) What is the frequency, f, in Hz of the photon emitted in this transition?

f = Hz.