m_l, the magnetic quantum number, is connected to the direction of the orbital angular momentum of the electron. Only particular directions of the angular momentum are allowed - this is known as space quantization. The direction of the orbital angular momentum is generally specified by stating its z-component. The allowed values are:

Lz = ml

h 2p

m_l is an integer between -l and +l

m_l = -l , ... , -1, 0, 1, ... , l

Why is this quantum number known as the magnetic quantum number? In the absence of a magnetic field all the energy levels with the same n and l values have the same energy. When a magnetic field is applied the energy levels split, with all the different m_l values giving slightly different energies. This splitting of the levels is known as the Zeeman effect.