# Zeeman Effect lab report Essay Example

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- Document type:Assignment
- Level:Undergraduate
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18Zeeman effect

Zeeman Effect lab report

**Introduction**

Zeeman Effect is a phenomenon exhibited when the energy levels of given atoms are split whenever an external magnetic field is placed in its vicinity. The interaction between the magnetic field B and the magnetic momentum _{} causes the relative orientation of their energies. The amount of energy is shifted in a relationship has an effect on the nuclear magnetic resonance (NMR). As noted by (Zettili, 2001), the splitting is dependent on the nuclear orientation and its static magnetic field.

The atoms are excited at levels that are above the ground state. Inherently, the quantum physics depicts that, the energies of particles presume certain specific values. In addition, the assertion of Pauli Exclusion Principle notes that, it is almost impossible for two electrons to presume the same state at a go. Electrons moving to a higher energy level would absorb energy, while those moving to lower energy level would lose energy. Zeeman’s effect would be experienced when a magnetic field is applied between the excited state and the ground state. This effect causes a slight emission of photons possessing different energies. The splitting of the magnitude would depend on the magnetic field.

**Theoretical background**

This phenomenon was discovered way back in 1896 by Zeeman-Lorentz hence its name. Efforts by faraday to proof the viability of whether there are changes accompanied in the spectrum of coloured flames when subjected to a magnetic deemed futile. A Bohr picture of an atom was used to elucidate the occurrence. An electron that is placed in a magnetic field would experience a Lorentz force which would tend to change the orbit of a given electron that exhibits its energy (Kenyon, 2011). The movement of the electron determines the change in the energy whether it is negative or positive depending on the motion of the electron. In cases where the field is along the plane of a given orbit, it follows that the Lorentz force exhibited would be zero and the corresponding change of energy would be zero. The assertion derived from this perspective dictates that, whenever a field is applied, the spectral emission would split into three lines. Arguably, it has been believed that, there exists a magnetic momentum of _{} emanating from the motion of a given orbital electron. Consequently, Zeeman splitting can be calculated from the Hamiltonian equation below. _{}. The splitting is dependent on the magnetic field orientation to its angular momentum. In the recent studies, it has been found out that, the electrons also possess an associated magnetic momentum_{}, angular momentum J and its orbital momentum. The electron spin has a Zeeman Effect of different magnitude as compared to the orbital angular momentum due to fact that, the spin electron possesses a magnetic momentum that is twice the orbital spin.

_{} It is the Lande g-factor found in the L-S coupled atom

The electron energy shift perturbation is exhibited as

_{Having B indicating the orientation of the Z axis}

_{Change n energy would be determined by }

_{}_{where }

The zeman splitting with the magnetic field in the z direction would be given as

This report considers the Zeeman splitting of mercury atoms of wavelengths 546.1 nm (_{}

**Experiment procedures**

*Apparatus*

Electromagnetic poles Cadmium lamp

Lens Etalon

Eye piece Polarizer

*Procedures*

Place the miniature mercury discharge tube in a magnetic gap so as it is at the centre of the tube. The optical components are supposed to be aligned in a common axis. This may be achieved by placing the cadmium lamp to warm for about five minutes. The lights in the room would be turned off after which the beam would be tested on a small path using a small piece of white paper. The Polaroid is set at 114^{o}bthen the spectrum of the mercury is recorded

Turn the magnet in order to have a current increase of about 10 amperes. This produces a stronger electromagnetic field over where light would be emitted. The Hall probe Gaussmeter aids in determining the real magnetic field strength. Measure the _{}of the mercury 546.7nm line. The hall probe would be used to measure the magnetic field.

Carefully measure the spectrum of the 3 or 4 other smaller magnetic fields.

The Fabry-Perot plates are aligned in parallel so as to achieve the required resolution.

Take the measurements of the _{} and _{} taking spectra having 1.5 T and a wavelength of mercury of 546.7nm. The mercury tube is then replaced with the neon discharge tube. The rheostat is then adjusted to be in series and placed to a transformer of high voltage.

Measure the polarization of the _{} and _{} of the 546.7nm spectrum line

*Answers to questions*

Tl. *When the spectral lines are viewed in the plane perpendicular to *

*, what are the polarisations associated with the *

* and *

* transitions?*

When* ,* the polarization spectral lines viewed -1/2. It appears to be parallel to the magnetic field. At *
*, the polarization spectral lines is at 3/2 and -2 respectively. They appear to be perpendicular to the magnetic field.

T2. *Calculate *

*for the *

* and *

* levels and construct an energy level diagram like that given for the 579.1nm line. Note that, since *

* you must enumerate the possible transitions VERY carefully*.

g=1+_{}=2

gf=1+_{}=_{}

J=5.788*10^{-5}

T3. *Calculate the unsplit and split frequencies for the **546.1nm** line assuming a magnetic field of *

*. What is the resolution in frequency *

* required to observe all the predicted splittings distinctly*?

=_{}=4.410^{14} Hz

*E 1. Show that the phase lag, *

*, between the beams emerging at *

& * is*

BC=Cos_{}

BE=BC Cos 2_{}

=_{}

=4_{}/_{} d cos_{}

Show that

A =

is called the Airy function.

R=_{}

The intensity of light is given

_{}_{m}=_{}_{}

*E3. Show that, assuming **** << 2 **** ,*

The FINESSE of the etalon is a measure of its resolution and is defined by

and the Airy formula can be written

By measuring the width, the frequency of the etalon may be determined using the corresponding *v* and so determine the frequency resolution of the etalon. R can also be estimated. The finesse is a vital determinant of the success of such an experiment.

E4. *Ascertain the current value for the setting of d, the etalon spacing, and calculate the free spectral range at *

= 546.1nm.

The current value should be atleast 10 amperes whereas the spectral range would be _{}

D=1.0cm, the FSR of 1.5_{} 10^{10}

, the rings at the focal plane will have radiiThe etalon is symmetric about the optical axis so the fringe pattern is circular. If the parallel beams emerging from the etalon are focussed by a lens of focal length

is called the ring order. Define for the nth ring. where

, show that for small E5. With the approximation

N=_{}

*E6. Show that the radius of the ring is given by*

_{} 1

And _{} 2

_{} 3

Combining equation 1, 2 and 3 we obtain

Therefore

for the split rings. against , from graphs of , in ), the frequency splitting between rings can be calculated by measuring the change, (or is just the frequency shift corresponding to a change of 1 in . Since the rings with different values of When the ring pattern is split by the Zeeman effect, the pth ring will split into 2 or more

E7. *Show that the frequency splitting is*

_{}^{-1}_{}

_{}f=FSR=_{}

_{}

In order to calculate the finesse you will measure the thicknesses of several rings.

E8. *Show that the full width of the ring is*

(6)

, soBut

From _{}_{}

We obtain

_{}— _{}=_{}

Therefore

References

Kenyon, R. (2011). *The light fantastic: A modern introduction to classical and quantum Optics*. Oxford: Oxford UP.

Zettili, N. (2001) *Quantum mechanics: Concepts and applications*. Chichester: Wiley.