Zeeman Effect lab report Essay Example

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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 Zeeman Effect lab report 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 Zeeman Effect lab report 1 emanating from the motion of a given orbital electron. Consequently, Zeeman splitting can be calculated from the Hamiltonian equation below. Zeeman Effect lab report 2. 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 momentumZeeman Effect lab report 3, 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.

Zeeman Effect lab report 4

Zeeman Effect lab report 5 It is the Lande g-factor found in the L-S coupled atom

Zeeman Effect lab report 6

The electron energy shift perturbation is exhibited as

Zeeman Effect lab report 7Zeeman Effect lab report 8Zeeman Effect lab report 9

Having B indicating the orientation of the Z axis

Change n energy would be determined by

Zeeman Effect lab report 10

where Zeeman Effect lab report 11

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

Zeeman Effect lab report 12

This report considers the Zeeman splitting of mercury atoms of wavelengths 546.1 nm (Zeeman Effect lab report 13

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 114obthen 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 Zeeman Effect lab report 14of 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 Zeeman Effect lab report 15 and Zeeman Effect lab report 16 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 Zeeman Effect lab report 17 and Zeeman Effect lab report 18 of the 546.7nm spectrum line

Zeeman Effect lab report 19

Answers to questions

Tl. When the spectral lines are viewed in the plane perpendicular to
Zeeman Effect lab report 20
, what are the polarisations associated with the
Zeeman Effect lab report 21
and
Zeeman Effect lab report 22
transitions?

WhenZeeman Effect lab report 23 , the polarization spectral lines viewed -1/2. It appears to be parallel to the magnetic field. At
Zeeman Effect lab report 24
, the polarization spectral lines is at 3/2 and -2 respectively. They appear to be perpendicular to the magnetic field.

T2. Calculate
Zeeman Effect lab report 25
for the
Zeeman Effect lab report 26
and
Zeeman Effect lab report 27
levels and construct an energy level diagram like that given for the 579.1nm line. Note that, since
Zeeman Effect lab report 28
you must enumerate the possible transitions VERY carefully.

g=1+Zeeman Effect lab report 29=2

gf=1+Zeeman Effect lab report 30=Zeeman Effect lab report 31

Zeeman Effect lab report 32

J=5.788*10-5

T3. Calculate the unsplit and split frequencies for the 546.1nm line assuming a magnetic field of
Zeeman Effect lab report 33
. What is the resolution in frequency
Zeeman Effect lab report 34
required to observe all the predicted splittings distinctly?

Zeeman Effect lab report 35

=Zeeman Effect lab report 36=4.4Zeeman Effect lab report 371014 Hz

E 1. Show that the phase lag,
Zeeman Effect lab report 38
, between the beams emerging at
Zeeman Effect lab report 39 & Zeeman Effect lab report 40
is
Zeeman Effect lab report 41

Zeeman Effect lab report 42

BC=CosZeeman Effect lab report 43

BE=BC Cos 2Zeeman Effect lab report 44

Zeeman Effect lab report 45

=Zeeman Effect lab report 46

Zeeman Effect lab report 47

=4Zeeman Effect lab report 48/Zeeman Effect lab report 49 d cosZeeman Effect lab report 50

Zeeman Effect lab report 51

Show that

Zeeman Effect lab report 52

Zeeman Effect lab report 53A =

is called the Airy function.

R=Zeeman Effect lab report 54

The intensity of light is given

Zeeman Effect lab report 55

Zeeman Effect lab report 56

Zeeman Effect lab report 57m=Zeeman Effect lab report 58Zeeman Effect lab report 59

E3. Show that, assuming  << 2 ,

Zeeman Effect lab report 60

Zeeman Effect lab report 61

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

Zeeman Effect lab report 62

Zeeman Effect lab report 63

and the Airy formula can be written

Zeeman Effect lab report 64

Zeeman Effect lab report 65

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 Zeeman Effect lab report 66

D=1.0cm, the FSR of 1.5Zeeman Effect lab report 67 1010

, the rings at the focal plane will have radiiZeeman Effect lab report 68The 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

Zeeman Effect lab report 69

is called the ring order. DefineZeeman Effect lab report 71 for the nth ring. Zeeman Effect lab report 70where

Zeeman Effect lab report 72

Zeeman Effect lab report 74 , show that for small Zeeman Effect lab report 73E5. With the approximation

Zeeman Effect lab report 75

N=Zeeman Effect lab report 76

Zeeman Effect lab report 77

E6. Show that the radius of the Zeeman Effect lab report 78 ring is given by

Zeeman Effect lab report 79

Zeeman Effect lab report 80 1

And Zeeman Effect lab report 81 2

Zeeman Effect lab report 82 3

Combining equation 1, 2 and 3 we obtain

Zeeman Effect lab report 83

Zeeman Effect lab report 84Therefore

for the split rings.Zeeman Effect lab report 93 against Zeeman Effect lab report 92 , from graphs of Zeeman Effect lab report 91 , in Zeeman Effect lab report 90 ), the frequency splitting between rings can be calculated by measuring the change, Zeeman Effect lab report 89 (or Zeeman Effect lab report 88 is just the frequency shift corresponding to a change of 1 in Zeeman Effect lab report 87 . Since the Zeeman Effect lab report 86 rings with different values of Zeeman Effect lab report 85When 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


Zeeman Effect lab report 94Zeeman Effect lab report 95-1Zeeman Effect lab report 96

Zeeman Effect lab report 97f=FSR=Zeeman Effect lab report 98

Zeeman Effect lab report 99

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

E8. Show that the full width of the Zeeman Effect lab report 100 ring is

(6)Zeeman Effect lab report 101

, soZeeman Effect lab report 102But

Zeeman Effect lab report 103

Zeeman Effect lab report 104

From Zeeman Effect lab report 105Zeeman Effect lab report 106

We obtain

Zeeman Effect lab report 107Zeeman Effect lab report 108=Zeeman Effect lab report 109

Therefore

Zeeman Effect lab report 110

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.