Concept explainers
The de Broglie wavelength of an electron if it has been accelerated through a potential difference of
Answer to Problem 42SP
Solution:
Explanation of Solution
Given data:
The electron is accelerated through the potential difference of
Formula used:
Write the expression for de Broglie wavelength:
Here,
Write the expression for the relativistic energy:
Also, the modified form of the relativistic energy is as follows:
The expression for the energy associated with a moving charge under influence of an electric field is
Here,
Explanation:
Recall the expression for the energy associated with a moving charge under influence of an electric field is
Recall the expression for the relativistic energy:
Understand the kinetic energy came into existence due to the electric field. Therefore, the kinetic energy will be equal to the energy associated with the charge particle due to the field.
Therefore,
Substitute
Combine the kinetic energy expression and the relativistic energy expression. Hence,
Also, the modified form of the relativistic energy is as follows:
Substitute
Further solving, we get
Convert potential difference MV into V
Recall the relativistic effect, the expression for the De Broglie wavelength of the electron is
Substitute
Conclusion:
The De Broglie wavelength of the electron is
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