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.
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.

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 |
Related Term(s)
Term(s) with "wavelength of electron" in the description


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