# Atomic Energy Levels in the Presence of a Magnetic Field

1. Jan 25, 2010

### MattLiverpool

1. The problem statement, all variables and given/known data

In the presence of a magnetic field, the energy of an atomic energy level is changed by the quantity:

Emag=g$$\mu$$BBM

(i) Expain the meaning of the terms in the expression.

(ii) Into how many levels is the ground state of the sodium atom split?

(iii) For each level calculate the change in energy in units of eV for an applied magnetic field of B=0.1T

2. Relevant equations

The ground state of a sodium atom has electronic configuartion

(1s)2(2s)2(2p)6(3s)

The land$$\acute{e}$$ factor is given by:

g=1+$$\frac{J(J+1)+S(S+1)-L(L+1)}{2J(J+1)}$$

3. The attempt at a solution

(i)

Emag is the magnetic energy
g is the Land$$\acute{e}$$ factor
$$\mu$$b is the magnetic moment
B is the magnetic field strength
M is the magnetic quantum number

(ii)

Split into (2J+1) levels

the

1s level has l = 0 hence J = 1/2 so splits into two levels
2s level has l = 0 hence J = 1/2 so splits into two levels
2p level has l = 1 hence J = 1 + 1/2 = 3/2 so splits into four levels
3s level has l = 0 hence J = 1/2 so splits into two levels

The ground state splits into eight levels.

I am unsure if this is the correct method to answer the question.

(iii)

Assuming (ii) was correct, I am unsure how to go from here, I assumed I could just subsitute into the Emag equation however I have no knowledge of M or $$\mu$$b.

Can anyone help me?!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution