No, when an electron absorbs a photon, its spin does not change to 3/2. The spin of an electron remains fixed at 1/2, regardless of the properties of the absorbed photon.
In quantum mechanics, the spin of a particle is an intrinsic property that characterizes its angular momentum. The spin of an electron is always quantized in units of ħ/2 (where ħ is the reduced Planck's constant), and it can take values of +1/2 or -1/2.
When an electron absorbs a photon, several things can happen depending on the specific interaction. The absorption of a photon can change the energy and momentum of the electron, leading to a different state, but it does not change the intrinsic spin of the electron.
The spin of a photon itself is always fixed at ±1, corresponding to right-handed or left-handed circular polarization, respectively. The spin of the photon is unrelated to the spin of the electron. The absorption of a photon by an electron does not alter the spin of the electron but can change its energy, momentum, or orbital angular momentum.
In summary, when an electron absorbs a photon, its spin remains at 1/2, and the absorbed photon's spin does not directly affect the spin of the electron.