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For what value of an electron’s speed will its de-Broglie wavelength be same as the compton wavelength? (in terms of c)
Correct answer is '0.707'. Can you explain this answer?
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For what value of an electron’s speed will its de-Broglie wavele...
de Broglie wavelength
Compton wavelength
The correct answer is: 0.707
Compton wavelength
The correct answer is: 0.707
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For what value of an electron’s speed will its de-Broglie wavele...
de Broglie wavelength
Compton wavelength
The correct answer is: 0.707
Compton wavelength
The correct answer is: 0.707
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For what value of an electron’s speed will its de-Broglie wavele...
De-Broglie Wavelength vs Compton Wavelength:
The de-Broglie wavelength is the wavelength associated with a particle, such as an electron, due to its momentum. On the other hand, the Compton wavelength is the wavelength associated with the rest mass energy of a particle.
Equations:
- De-Broglie Wavelength: λ = h / p, where h is the Planck constant and p is the momentum of the particle.
- Compton Wavelength: λc = h / (mc), where m is the rest mass of the particle and c is the speed of light.
Setting the Wavelengths Equal:
To find the speed at which the de-Broglie wavelength is equal to the Compton wavelength, we set the two equations equal to each other:
h / p = h / (mc)
Solving for Speed:
By substituting the momentum p = mv (where v is the speed of the particle) into the de-Broglie wavelength equation, we get:
h / mv = h / (mc)
Solving for v, we get:
v = c / √2 ≈ 0.707c
Therefore, when the speed of the electron is approximately 0.707 times the speed of light, its de-Broglie wavelength will be equal to the Compton wavelength.
The de-Broglie wavelength is the wavelength associated with a particle, such as an electron, due to its momentum. On the other hand, the Compton wavelength is the wavelength associated with the rest mass energy of a particle.
Equations:
- De-Broglie Wavelength: λ = h / p, where h is the Planck constant and p is the momentum of the particle.
- Compton Wavelength: λc = h / (mc), where m is the rest mass of the particle and c is the speed of light.
Setting the Wavelengths Equal:
To find the speed at which the de-Broglie wavelength is equal to the Compton wavelength, we set the two equations equal to each other:
h / p = h / (mc)
Solving for Speed:
By substituting the momentum p = mv (where v is the speed of the particle) into the de-Broglie wavelength equation, we get:
h / mv = h / (mc)
Solving for v, we get:
v = c / √2 ≈ 0.707c
Therefore, when the speed of the electron is approximately 0.707 times the speed of light, its de-Broglie wavelength will be equal to the Compton wavelength.
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For what value of an electron’s speed will its de-Broglie wavelength be same as the compton wavelength? (in terms ofc)Correct answer is '0.707'. Can you explain this answer?
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For what value of an electron’s speed will its de-Broglie wavelength be same as the compton wavelength? (in terms ofc)Correct answer is '0.707'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about For what value of an electron’s speed will its de-Broglie wavelength be same as the compton wavelength? (in terms ofc)Correct answer is '0.707'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of an electron’s speed will its de-Broglie wavelength be same as the compton wavelength? (in terms ofc)Correct answer is '0.707'. Can you explain this answer?.
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