I can not get convinced why for energy level, filled with an even number of electrons, the net magnetic moment is zero! If we have a level with the quantum number l, we have two electrons with opposite spins in it. Also magnetic moment is proportional to Jtotal where [itex]J_t= J_1+J_2[/itex](1and 2 refer to electrons). Moreover [itex]J=L+S[/itex]. If magnetic moment were to be zero, the [itex]J_t[/itex] must be zero. How can we show that?