# Charge-to-mass ratio with Zeeman Effect

• tuomas22
In summary, the conversation is discussing how to determine e/m using the Zeeman effect with a given magnetic field of 0.45 T and a known difference between two spectral lines (0.649x10^10 Hz). The equations for normal and anomalous Zeeman effects are mentioned, and the attempt at a solution includes calculating m_l using the equation 2l+1. However, there is uncertainty about how to obtain l from the given data.
tuomas22

## Homework Statement

I'm supposed to determine e/m using Zeeman effect.
B=0.45 T
Difference between two spectral lines is also known (0.649x10^10 Hz)

## Homework Equations

Normal or anomalous Zeeman effect? How you know it?
I'm guessing normal, so
$$\Delta E = m_{l} \frac{e \hbar}{2m_{e}}B$$

$$\Delta E = h \Delta f$$

so,

$$\frac{e}{m_{e}} = \frac{h \Delta f2m_{e}}{m_{l} \hbar B}$$

## The Attempt at a Solution

Well the attempt at solution is the equations I just wrote, are they right so far?

But the problem is, how I get $m_{l}$? I think it's $$2l+1$$, but how I get $l$ from the know data then?

Last edited:
any tip would be much appreciated, I got exam tomorrow and I want to understand this :P

## 1. What is charge-to-mass ratio?

Charge-to-mass ratio is a physical quantity that represents the ratio of the electric charge of a particle to its mass. It is commonly denoted by the symbol q/m and is measured in units of coulombs per kilogram (C/kg). This ratio is used to describe the behavior of charged particles in electric and magnetic fields.

## 2. How is charge-to-mass ratio measured?

The charge-to-mass ratio can be measured using various techniques such as the Thomson method, the Millikan oil drop experiment, and the cyclotron resonance method. These methods involve applying known electric and magnetic fields to a charged particle and measuring its acceleration or deflection. By comparing the results to the known values of the fields, the charge-to-mass ratio can be determined.

## 3. What is the Zeeman effect?

The Zeeman effect is the splitting of spectral lines in the presence of a magnetic field. This phenomenon was first observed by Dutch physicist Pieter Zeeman in 1896 and is caused by the interaction between the magnetic field and the magnetic dipole moment of the atoms or molecules. The effect is used in spectroscopy to study the energy levels of atoms and molecules.

## 4. How does the Zeeman effect relate to charge-to-mass ratio?

The Zeeman effect can be used to determine the charge-to-mass ratio of an electron. By applying a known magnetic field and observing the splitting of spectral lines, the magnetic dipole moment of the electron can be calculated. This, combined with the known charge of the electron, allows for the determination of the charge-to-mass ratio.

## 5. What are the applications of charge-to-mass ratio and Zeeman effect?

The charge-to-mass ratio and Zeeman effect have a wide range of applications in physics and engineering. They are used in particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. They are also important in understanding the behavior of charged particles in space, such as in the Earth's magnetic field and in the study of cosmic rays.

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