# Calculating Lande g-Factor for 3S1, 3P0, 3P1, 3P2 States

• neu
In summary: I'm getting very lost. In summary, the g-factor for the 3S1, 3P0, 3P1, and 3P2 states is equal to 3, but if the J-value is equal to L+S, the g-factor is not equal to 1.
neu
Im getting very confused about how to calculate the lande g-factor for the 3S1, 3P0, 3P1, and 3P2 states

I know its equal to

http://www.pha.jhu.edu/~rt19/hydro/img208.gif

but if i have state 3P0 where S=1 as 2S+1 = 3 and L=P=1 and J=0, but J=L+S which isn't =1?

I've read myself into a hole can someone help us out?

I should say the g-value is used in the zeeman effect. Gives the energy shift as ratio of bohr magneton

http://www.pha.jhu.edu/~rt19/hydro/img207.gif

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neu said:
Im getting very confused about how to calculate the lande g-factor for the 3S1, 3P0, 3P1, and 3P2 states

I know its equal to

but if i have state 3P0 where S=1 as 2S+1 = 3 and L=P=1 and J=0, but J=L+S which isn't =1?

I've read myself into a hole can someone help us out?
J = L±S yes?

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Why would you need to calculate it if there is no electron at that energy level? Guess I'm missing something.

neu said:
Im getting very confused about how to calculate the lande g-factor for the 3S1, 3P0, 3P1, and 3P2 states

I know its equal to

http://www.pha.jhu.edu/~rt19/hydro/img208.gif

but if i have state 3P0 where S=1 as 2S+1 = 3 and L=P=1 and J=0, but J=L+S which isn't =1?

I've read myself into a hole can someone help us out?

Just plug in the values of S,L and J.

Your problem does not seem to be in finding g but in vector addition in QM. Recall that in QM, writing ${\vec J } = {\vec L } + {\vec S}$ means that J will range from |L-S| to |L+S| in steps of 1. So, if S=1 and L=1, J could take any value between |1-1| and |1+1| so J may be equal to 0, 1 or 2. Your 3P0, 3P1 and 3P2 states correspond to those three possible values of J.

Hope this makes helps.

Patrick

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Thats exactly the clarity i needed thankyou

I'm stuck with calculating g and p for Eu(3+).

The outtermost orbitals in Eu is 4f7 5s2 5p6 6s2. Eu(3+) has 4f6 as the last orbital.

Thus, S = 3, L = 3 and J = 0 since J = L - S here.

How do I calculate g (using the formula given above) and then p. (p = g[S(S+1)]).

The experimental value for p = 3.4 and I read that g must be 2 in this case.

I am at a loss how to arrive at this result.

Can anyone help?

## 1. What is the Lande g-factor?

The Lande g-factor, also known as the Landé g-factor or the spectroscopic splitting factor, is a dimensionless quantity that describes the magnetic moment of an electron or nucleus in an atom relative to its angular momentum. It is used to determine the energy levels and spectral lines of atoms in the presence of an external magnetic field.

## 2. How is the Lande g-factor calculated?

The Lande g-factor is calculated using the formula g = 1 + (J(J+1) + S(S+1) - L(L+1)) / (2J(J+1)), where J, S, and L represent the total, spin, and orbital angular momentum quantum numbers, respectively. This formula can be applied to different energy states of an atom, such as the 3S1, 3P0, 3P1, and 3P2 states.

## 3. What are the factors that affect the Lande g-factor?

The main factors that affect the Lande g-factor are the spin and orbital angular momenta of the electron or nucleus, the strength of the external magnetic field, and the relativistic effects of the atom. These factors can change the energy levels and spectral lines of an atom, making the calculation of the Lande g-factor important for studying atomic structure and behavior.

## 4. Why is the Lande g-factor important in atomic physics?

The Lande g-factor is important in atomic physics because it helps to explain and predict the behavior of atoms in the presence of a magnetic field. It is also a key factor in understanding the Zeeman effect, which is the splitting of spectral lines in a magnetic field, and the hyperfine structure of atomic energy levels. Additionally, the Lande g-factor is used in many experimental techniques for studying atoms and molecules.

## 5. How does the Lande g-factor differ for different energy states?

The Lande g-factor can differ for different energy states of an atom because the values of J, S, and L can vary between states. This is due to the different arrangements of electrons in the atom's energy levels, which can affect the spin and orbital angular momenta. Therefore, the Lande g-factor may be different for the 3S1, 3P0, 3P1, and 3P2 states, which have different quantum numbers and energy levels.

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