Final answer:
An electro with angular momentum quantum number l=2 in a 3 T magnetic field along the z-direction experiences energy level splitting into five components due to the Zeeman effect, with the values of −l to l in steps of one for the angular momentum projection quantum number.
Step-by-step explanation:
When an atomic electron with an angular momentum quantum number l=2 is placed in a magnetic field of 3 T along the z-direction, the energy levels of the atom split due to the Zeeman effect. This effect quantizes the direction of angular momentum, meaning that the z-component of angular momentum can have only certain values equal to ml × (h/2π), where h is the reduced Planck's constant and ml is the angular momentum projection quantum number.
For l=2, ml can have the values −l to l in steps of one, i.e., −2, −1, 0, 1, 2. So, the energy level splits into five components. The separation between these levels, which is related to the splitting of spectral lines into discrete parts, depends on factors such as the magnetic field strength, g-factor, and the reduced Planck's constant.