# Drawing the Zeeman Spectrum in Magnesium

• Yaste
In summary, a Zeeman experience was conducted in Magnesium with a magnetic field of 2Teslas, resulting in an emission at 518.360nm. Using equations for energy and spin, the deviations of the observed lines in units of GHz were calculated. The problem also involved drawing the allowed transitions on a spectrum using the selection rules. This is considered an anomalous Zeeman effect because it includes spin in the calculations for energy.
Yaste

## Homework Statement

A zeeman experience is made in the transition 3s4s ## ^3S_1## -> 3s3p ##^3P_2## in Magnesium with a magnetic field of 2Teslas (20 000 Gauss). With no magnetic field the emission occurs in 518.360nm.

a) Draw the spectrum of what you hoped you observe when you're watching the system in a direction parallel to the applied magnetic field.
b) What are the deviations of the observed lines in units of GHz?

## Homework Equations

$$\Delta E = g_J \mu_B M_J B$$

$$g_J = \frac{3}{2} + \frac{S(S+1)-L(L-1)}{2J(J+1)}$$

## The Attempt at a Solution

The term ## ^3S_1## has S=1, L=0 and J =1 and ##^3P_2## has S=1, L=1, J=2. So we have ##\Delta L =1##, ##\Delta S =0## and ##\Delta J =1##. Using the following equations I can have the deviations of the observed lines in Joules:

$$\Delta E = g_J \nu_B M_J B$$

$$g_J = \frac{3}{2} + \frac{S(S+1)-L(L-1)}{2J(J+1)}$$

After that, I can use ##E=h/\nu## to find the frequency. Those are the deviations between the sub-lines of ## ^3S_1## and ##^3P_2##, right? I mean, these lines are going to have 3 (##M_J=1,0,-1##) and 5 (##M_J=2,1,0,-1,-2##) sub-lines, respectively.

I have, however, no idea how to solve a)! Would be very thankful for any help.

Last edited:
For part (a), what are the allowed transitions? Draw them on a spectrum in units of ##Ghz##?

Yaste
You will need the selection rules. Also, this is the anomalous zeeman effect, not the normal zeeman effect.

unscientific said:
You will need the selection rules. Also, this is the anomalous zeeman effect, not the normal zeeman effect.

I was able to solve the problem. One question though: Why is it an anomalous zeeman effect?

Yaste said:
I was able to solve the problem. One question though: Why is it an anomalous zeeman effect?
Because spin is included (check formula for ##g_J##).

## 1. What is the Zeeman effect?

The Zeeman effect is the splitting of spectral lines in an atom's emission or absorption spectrum due to the presence of a magnetic field. This effect was first observed by Dutch physicist Pieter Zeeman in 1896.

## 2. Why is studying the Zeeman effect important in understanding atomic structure?

The Zeeman effect provides valuable information about the energy levels and electron configurations of atoms. By observing the splitting of spectral lines, scientists can determine the strength of the magnetic field and the properties of the atom's electrons.

## 3. How is the Zeeman spectrum in magnesium drawn?

The Zeeman spectrum in magnesium is typically drawn using a diagram known as a magnetograph. This diagram shows the energy levels of the atom and the resulting spectral lines when a magnetic field is applied. Each spectral line is labeled with its corresponding energy level and the direction of the magnetic field.

## 4. What factors can affect the Zeeman spectrum in magnesium?

The strength of the magnetic field, the temperature of the atom, and the orientation of the magnetic field relative to the atom can all affect the Zeeman spectrum in magnesium. Additionally, the number of electrons and their energy levels in the atom can also impact the spectrum.

## 5. How is the Zeeman spectrum in magnesium used in practical applications?

The Zeeman spectrum in magnesium is used in various fields such as astronomy, chemistry, and physics. It can help in identifying elements in stars, studying the structure of atoms, and understanding the behavior of electrons in magnetic fields. It is also useful in spectroscopy, a technique used to determine the chemical composition of substances.

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