Deuterium atom Consider a deuterium atom composed of a spon1

Deuterium atom Consider a deuterium atom composed of a spon-1 deuteron and a spin -1/2 electron. The totle electronic angular monentum is where I is the orbital angular momentum of the electron and s is its spin. The total angular momentum of the atom is where I is the nuclear spin The eigenvalues of J^2 and F^2 are J(J+1) h^2 and F(F+1)h^2, respecyively What are the possible values of the guantum numbers J and F for a deuterium atom in the is ground state? What are the possion values of the guantum numbers J and F for a deuterium atom in the 2p excited state?

Solution

Answer:

In 1s ground state, for deuterium

for 1s state the value of l = 0, S = 1 (triplet)

possible valuse of J = mode of (L+S) to mode of (L-S)

J = 1,

The eigen values of J² is J(J+1)(h/2pi)² = 2 (h/2pi)²

possible values of F = mode of (J+I) to mode of (J-I) Nuclear spin quantum no. I = 1 for deuterium

F = 2, 1, 0

The eigen values of F² are    6(h/2pi)² and 2 (h/2pi)²

In 2p ground state, for deuterium

l =1, s = 0 (singlet)

J = 1

The eigen values of J² is J(J+1)(h/2pi)²   = 2 (h/2pi)²

So for the F²

The eigen values of F² are    6(h/2pi)² and 2 (h/2pi)²