The normalised wave functions for an electron in a simplified model of the hydrogen atom have the form:

_n,l,m (r, , , t) = (u(r)/r)Y_l,m(, )e^-iE_nt/

where m should be m_l (won't allow me to double subscript).

(a) State the allowed values of n, l and m_l for this wave function and give an equation for a physical quantity that can be calculated from each quantum number.

(b) Show that the probability distribution for the radial position of the electron is P(r)dr = u²dr.

(c) A beam of silver atoms passes through a non-uniform magnetic field (Stern-Gerlach experiment).

i. What is the reason for using a non-uniform magnetic field in the Stern-Gerlach experiment?

ii. What is the effect of the non-uniform magnetic field on atoms with l = 0?

iii. Which property of electrons is indicated by the results of this experiment?

iv. What effect does this property of electrons have on the energy levels for electrons in hydrogen atoms?