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Objectives:: Experiment

This experiment aimed to verify the de Broglie hypothesis that electrons exhibit wave-like properties and can be diffracted. An electron beam was directed at a graphite target and the diffraction pattern was analyzed. Bragg's law was applied to calculate the wavelength of the electrons from the radii of diffraction rings. The interplanar spacings of graphite were evaluated and found to have errors of 14.6% and 12.1% compared to theoretical values.

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ضياء بن احمد الكباري
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124 views3 pages

Objectives:: Experiment

This experiment aimed to verify the de Broglie hypothesis that electrons exhibit wave-like properties and can be diffracted. An electron beam was directed at a graphite target and the diffraction pattern was analyzed. Bragg's law was applied to calculate the wavelength of the electrons from the radii of diffraction rings. The interplanar spacings of graphite were evaluated and found to have errors of 14.6% and 12.1% compared to theoretical values.

Uploaded by

ضياء بن احمد الكباري
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Experiment (2):

Electron diffraction
 Objectives:
1. Verification de Broglie law.
2. Calculate the wavelength for electron beam
3. Studying the crystal structure for graphite and
evaluating the interplanar distances between the lattice planes

 Tools:
1. Electron diffraction tube
2. High voltage power supply

 Theory:
Louis de Broglie originated the idea that moving electrons may exhibit
both particle and wave nature. He proposed that, analogous to photons. If
electrons act like waves, we should be able to apply Bragg’s Law to the
diffraction of electrons. In that case the beam would appear as concentric
rings around a bright. This experiment involves directing a beam of
electrons through a carbon target, scattering the electrons, and analyzing
the pattern produced on a luminescent screen.
Bragg's presented a simple explanation of the diffracted beams from a
crystal. Suppose that the incident waves are reflected speculary form
parallel planes of atoms in the crystal. The diffracted beams are found when
the reflections from parallel planes of atoms interfere constructively and
that occur when:
2𝐿ℎ 1
𝐷=
𝑑 √2𝑚𝑒 √𝑣

such that,
e: electron charge
h: blank constant
m: mass of the particle
L: distance between sample and screen (0.135 m)
Experiment procedure:
1. connect the electron diffraction tube to its power supplies.
2. Ground the positive pole on the high-voltage power supply 10 kV.
3. Set the potential difference between the cathode and anode to
5.0kV.
4. Measure the diameters D1 and D2 and then the radius of the two
concentric rings observed.
5. Decrease the potential by 0.5 kV and repeat same step
6. Tabulate your results

Complete the table:


1 𝐷𝑑 𝐷𝑑
V(kv) D1st(cm) D2nd(cm) 𝜆1𝑠𝑡 = 𝜆2𝑛𝑑 =
√𝑣 2𝐿 2𝐿

2 0.022 3.6 6.3 2 ∙ 4 × 10−7 2 ∙ 6 × 10−7

3 0.018 3 5.5 2 ∙ 0 × 10−7 2 ∙ 3 × 10−7

4 0.015 2.4 4.4 1 ∙ 6 × 10−7 2 ∙ 1 × 10−7

5 0.014 2.2 4 1 ∙ 5 × 10−7 1 ∙ 6 × 10−7

Calculating:

From the plot of D and 1⁄ the slope of the two lines is:
√𝑣
Slope D1 = 175.9763
Slope D2 = 288.6673

So, the values of d1 and d2 can be calculated using:


2𝐿ℎ 3.2×10−10
𝑑= =
𝑠𝑙𝑜𝑝𝑒
𝑠𝑙𝑜𝑝𝑙𝑒 √2𝑚𝑒

3.2×10−10
𝑑1 = 175.9763
= 1 ∙ 8184 𝐴°
3.2×10−10
𝑑2 = 288.6673
= 1 ∙ 1085 𝐴°
The error percentage is:
The theoretical values for the interplanar spacing are:
d1 = 2.13 A֯
d2 = 1.23 A֯
The practical values for the interplanar spacing are:
d1 = 1.8184 A֯
d2 = 1.1085 A֯
2∙13−1∙8184
𝑒𝑟𝑜𝑟𝑟 𝑜𝑓 𝑑1 = 2.13
× 100% = 14 ∙ 629%

1∙23−1∙1085
𝑒𝑟𝑜𝑟𝑟 𝑜𝑓 𝑑2 = 1.23
× 100% = 12 ∙ 15%

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