Lab 6

Semiconductor Diodes

And

Zeeman Effect

 

 

 

 

Bill Chun Wai Hung

Nimish Kumar

Marjan Montakhab

 

Friday Section

 

20 May 2004

Marjan Montakhab

Physics 4D – Lab 6

Dr. Jordan

 
The Zeeman effect of the l =5461 A? Line of Hg (green)
 
GOAL:
           To measure the splitting of a degenerate
energy level of Mercury by applying a magnetic field. 
To identify the number of angular momentum states
experimentally. 
Equipment: 
 
The choice of the green line is due to its
predominance in the mercury spectrum and it is easy to
observe. In an external magnetic field, Hg is split
into nine components, in the lab a polarizer parallel
to the magnetic field was used, so that only three of
the nine components (the p light) appeared.
        The etalon and lenses are all mounted on an optical
bend to which the spectrograph is rigidly attach? The
pair of lenses L1 forms the light from the source into
the parallel beam. While the pair L2 focuses the
Fabry-Perot ring pattern on the spectrograph slit the
effective focal length of L2 is 8 cm and a further
magnification of 2 takes place in the spectrograph. 
        The spacing of Fabry-Perot etalon is t = 0.5002 cm.
The final adjustment is made by removing L3 so that
the observer locates his eye at F or mirror can be
used. The frings of equal width do appear parallel to
the base of the wedge that is formed by the two
plates. As the plates are moved in the parallelism,
the frings become border and finally the whole image
of the aperture seems to have a uniform elimination
(bright or dark) depending on the exact value of   n0
=   2t / l .
 
 
Data on Zeeman Effect:
 
        The source contains a single isotope, and the
polarizer allows only the observation of p light. When
the field is appealed the single line pattern brakes
up into triplet, the separation between the components
of the triplet becomes larger with increasing field.
If we first analyze the exposure with zero field to
verify that the squares of the radii do indeed follow:
 
 
                                                     ?the radii of the ring
 
The squares of the radii of adjacent rings are
constants.
 
And the fraction of an order _ can be found by
extrapolating to rp2 = 0 (according to the slope 2f2 /
n0 ).
        We will find the fractional order at the origin by
making a list squares fit to the squares of the radii.
The initial step in the reduction of the data is the
measurement of the
 diameter (or radii) of the rings. When the fringes in
the pattern are not broad enough, it is much more
accurate to measure the two edges and take the average
rather than try to set the crosshairs in the center of
the fringes. A more advance technique for obtaining
the ring diameter from the plates is to use a micro
photometer. 
 
Data Analysis of Fit Zeeman Effect
Ring P  A,B,C   Radius Rp (mm) Rp2     (Rp+12 - Rp2 )
1       A       6       36      1020.25
1       B       15      225     965.25
1       C       22      484     885
2       A       32.5    1056.25 968.75
2       B       34.5    1190.25 972
2       C       37      1369    1032
3       A       45      2025    N/A
3       B       46.5    2162.25 N/A
3       C       49      2401    N/A
 
 
Calculation:
1. Experimental Value Calculation
 
 This is the equation of the experimental value
Since 
 
h=6.626x10-34 J.S
c=3x108 m/s
 
 
In other words, if  , d,  , and   are known, the  can
be determined, and in turn, the experimental  can be
determined.
Since 
 
Given,
 =1.483,
d=6.020mm,
 = -153.41mm, and
 =994.5mm
So, 
 
By subsitituing   into the energy equation,
 
 
2. Theoretical Value Calculation
 
Given B is 4000G or 0.4 T
 
= (9.2732 x 10-24)(0.4T)      This is the equation of
the theoretical value
=3.70928 x 10-24 J
3.The Percentage Difference

 

The Zeeman effect of the l =5461 A° Line of Hg (green)

 

GOAL:

           To measure the splitting of a degenerate energy level of Mercury by applying a magnetic field.  To identify the number of angular momentum states experimentally.  To determine the characteristic function of the diode (current versus voltage) of a p-n diode. 

 

Equipment:

 

The choice of the green line is due to its predominance in the mercury spectrum and it is easy to observe. In an external magnetic field, Hg is split into nine components, in the lab a polarizer parallel to the magnetic field was used, so that only three of the nine components (the p light) appeared.

        The etalon and lenses are all mounted on an optical bend to which the spectrograph is rigidly attaché. The pair of lenses L1 forms the light from the source into the parallel beam. While the pair L2 focuses the Fabry-Perot ring pattern on the spectrograph slit the effective focal length of L2 is 8 cm and a further magnification of 2 takes place in the spectrograph.

        The spacing of Fabry-Perot etalon is t = 0.5002 cm. The final adjustment is made by removing L3 so that the observer locates his eye at F or mirror can be used. The frings of equal width do appear parallel to the base of the wedge that is formed by the two plates. As the plates are moved in the parallelism, the frings become border and finally the whole image of the aperture seems to have a uniform elimination (bright or dark) depending on the exact value of   n0 =   2t / l .

This is the equation of the experimental value

Since

h=6.626x10-34 J.S

c=3x108 m/s

 

 

 

 

 

 

Data on Zeeman Effect:

 

        The source contains a single isotope, and the polarizer allows only the observation of p light. When the field is appealed the single line pattern brakes up into triplet, the separation between the components of the triplet becomes larger with increasing field. If we first analyze the exposure with zero field to verify that the squares of the radii do indeed follow: 

 

                                                        à the radii of the ring

 

The squares of the radii of adjacent rings are constants.

 

And the fraction of an order ∊ can be found by extrapolating to rp2 = 0 (according to the slope 2f2 / n0 ).

        We will find the fractional order at the origin by making a list squares fit to the squares of the radii. The initial step in the reduction of the data is the measurement of the diameter (or radii) of the rings. When the fringes in the pattern are not broad enough, it is much more accurate to measure the two edges and take the average rather than try to set the crosshairs in the center of the fringes. A more advance technique for obtaining the ring diameter from the plates is to use a micro photometer.

 

 

 

Data Analysis of Fit Zeeman Effect

Ring P

A,B,C

Radius Rp (mm)

Rp2

(Rp+12 - Rp2 )

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data:

Forward Direction

I(A)

V(V)

R(Circuit) (Ohm)

2.94E-08

0.189

1.5556E-07

3.56E-08

0.194

1.8351E-07

8.01E-08

0.376

2.1303E-07

2.03E-07

0.434

4.6774E-07

5.94E-07

0.478

1.2427E-06

6.34E-07

0.501

1.2655E-06

9.34E-07

0.523

1.7859E-06

1.34E-06

0.533

2.5141E-06

1.56E-06

0.537

2.905E-06

 

Graph I.

 

Backward, Naive

V (R) (V)

V(D)(mV)

I (A)

R(Circuit) (Ohm)

0.80925

20.237

5.395E-08

375106580

1.26329

13.107

8.4219E-08

155629349

2.08517

9.573

1.3901E-07

68864888.7

3.0973

35.927

2.0649E-07

173991864

4.3567

45.32

2.9045E-07

156035531

5.8395

54.67

3.893E-07

140431544

6.346

59.674

4.2307E-07

141051056

7.2467

70.926

4.8311E-07

146810272

8.6257

90.374

5.7505E-07

157159419

9.0295

101.574

6.0197E-07

168736918

 

Backward, Improved

V (R) (V)

V(D)(mV)

I (A)

R(Circuit) (Ohm)

2.00925

11.736

1.3395E-07

87614781.6

2.26331

15.107

1.5089E-07

100121062

2.88534

30.573

1.9236E-07

158939674

3.6945

33.875

2.463E-07

137535526

4.689

42.32

3.126E-07

135380678

5.3313

53.23

3.5542E-07

149766473

6.124

56.23

4.0827E-07

137728609

7.3984

80.234

4.9323E-07

162671659

8.2498

89.823

5.4999E-07

163318505

8.4235

113.329

5.6157E-07

201808631

 

Graph 2.

Calculation:

The Resistant Across the DMM:

V1 = Voltage across the voltage source and the DMM = 22.370V

V2 = Voltage across the voltage source, the DMM, and the 15MW resistor (Rs)= 9.9951V

V = V1 – V2 = 22.370V - 9.9951V = 12.3749V

I = Current of the whole circuit =

Rm = Resistant of the DMM =

The Manufacture Value is 11M

The Percentage Difference is

 

 

 

Conclusion by Bill Chun Wai Hung:

The Turn on Voltage is the voltage which the semiconductor just start to conduct electricity because of the potential difference.

 

From the forward bias graph (Graph I), the turn on voltage is about 0.530.02V

 

For the backward bias graph (Graph 2), both the blue line is the naïve case, and the red line is the improved case. Both the naïve and the improved case produce a curve which the data “flatten” as the voltage increases. This is because as the voltage increases in the backward direction, the energy gap widened, and the current is less likely to pass through the diode.

 

The lowest resistant measured in the forward direction is 1.56 x 10^-7W, and the highest resistant measured in the backward direction is 87614781.6W.

 

During the experiment, the resistance or the DMM is measured to be 12.1MW, and the manufacture value is 11MW, the percentage difference is 10%.

 

Error Analysis

The relationship between current and voltage is exponential, so the error in voltage will cause a corresponding exponential error in the current

 

The reading of the voltage fluctuates and seldom really state at a concrete value, so the reading of current and voltage may be off by 0.5V for the voltage and 1% for the readings of current.