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The speed of an electron, whose de Broglie wavelength is equal to its Compton wavelength, is (C is the speed of light)
- a)c/√3
- b)c/√2
- c)c/2
- d)c/3
Correct answer is option 'B'. Can you explain this answer?
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The de Broglie wavelength of an electron is given by the equation:
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the electron.
The Compton wavelength of an electron is given by the equation:
λ_c = h / (m_e * c)
Where λ_c is the Compton wavelength, m_e is the mass of the electron, and c is the speed of light.
If the de Broglie wavelength is equal to the Compton wavelength, then we can set the two equations equal to each other:
h / p = h / (m_e * c)
Cancelling out the Planck constant, we get:
1 / p = 1 / (m_e * c)
Solving for p:
p = m_e * c
The momentum of the electron is equal to its mass multiplied by the speed of light. Since the mass of an electron is constant, the speed of the electron must be equal to the speed of light:
v = c
Therefore, the speed of the electron is c, which is the speed of light.
λ = h / p
Where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the electron.
The Compton wavelength of an electron is given by the equation:
λ_c = h / (m_e * c)
Where λ_c is the Compton wavelength, m_e is the mass of the electron, and c is the speed of light.
If the de Broglie wavelength is equal to the Compton wavelength, then we can set the two equations equal to each other:
h / p = h / (m_e * c)
Cancelling out the Planck constant, we get:
1 / p = 1 / (m_e * c)
Solving for p:
p = m_e * c
The momentum of the electron is equal to its mass multiplied by the speed of light. Since the mass of an electron is constant, the speed of the electron must be equal to the speed of light:
v = c
Therefore, the speed of the electron is c, which is the speed of light.
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