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wavelength of electron

wavelength of electron

wavelength of an electron is calculated for a given energy (accelerating voltage) by using the de Broglie relation between the momentum p and the wavelength λ of an electron (λ=h/p, h is Planck constant). As a result, the wavelength of an electron λ is expressed by the following first equation, where m0 is the rest mass of an electron, e is the elementary charge of an electron, E [V] is the accelerating voltage before the relativistic correction, and E* [V] is the accelerating voltage after the relativistic correction. The velocity v [m/s] of an electron under the accelerating voltage E [V] is expressed by the following second equation.
Table 1 shows a comparison list between the accelerating voltage E, the accelerating voltage after the relativistic correction E*, the wavelength of an electron λ, the velocity of an electron v, and the ratio of the velocity of an electron to the velocity of light β=v/c.
 
wavelength of electron
 
Table 1
Accelerating voltage
E[kV]
Relativistically corrected accelerating voltage E*[kV] Wavelength of electron
λ[pm]
Velocity of electron
v[m/s]
Ratio to the speed of light c
β = v/c
1 1.0010 38.764 1.8728E+07 0.06247
10 10.098 12.205 5.8455E+07 0.19499
20 20.391 8.5885 8.1503E+07 0.27187
30 30.881 6.9791 9.8445E+07 0.32838
40 41.566 6.0155 1.1214E+08 0.37406
60 63.523 4.8661 1.3377E+08 0.44622
80 86.262 4.1757 1.5062E+08 0.50240
100 109.78 3.7014 1.6435E+08 0.54822
120 134.09 3.3492 1.7588E+08 0.58667
160 185.05 2.8510 1.9430E+08 0.64811
200 239.14 2.5079 2.0845E+08 0.69531
300 388.06 1.9687 2.3280E+08 0.77653
400 556.56 1.6439 2.4819E+08 0.82787
500 744.62 1.4213 2.5868E+08 0.86286
1000 1978.5 0.87192 2.8213E+08 0.94108
1250 2778.9 0.73571 2.8689E+08 0.95697
2000 5913.9 0.50432 2.9352E+08 0.97907
3000 11806 0.35693 2.9660E+08 0.98935

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