Question

What are the values for the spin-angular-momentum and the orientation of the spin- angular-momentum for a ground-state hydrogen electron? Sketch a picture to display the electron orientation.

Answer 1

The value of the spin angular momentum of an electron

S = (h/2π)√{s(s+1)} = (√3/2) (h/2π)              [value of s for an electron = 1/2]

The proton in the center on the H atom has a spin 1/2. The two spins of electron and proton create magnetic dipole moments. the difference in energy between electron spin states is due to the interaction of those magnetic dipoles. Thus spin angular quantum no is quantized in space. It can have two orientations (m_s) in the space, the two possible values are +(1/2) or -(1/2). It specifies the orientation of the spin axis of an electron. An electron can spin in only one of two directions. The configuration with antiparallel magnetic moments(of proton and electron) has lower energy. Due to the negative charge in electron the orientation of the magnetic moment is opposite to its spin therefore antiparallel magnetic moments means parallel spins of proton and electron. Thus if the spin of the proton is taken as 'spin-up', ground state electron spin orientation will be +(1/2).