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An electron and a proton have same de-Broglie's wavelength. The kinetic energy of an electron is
- a)infinity
- b)zero
- c)equal to that of proton
- d)greater than that of proton
Correct answer is 'D'. Can you explain this answer?
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An electron and a proton have same de-Broglie's wavelength. The kineti...
As electron and proton have same de Broglie wavelength then the electron must have more more velocity as compared to proton because there momentum will be same Nd mass of proton is greater than mass of electron so.....we know k.E =1/2mv^2 or 1/2(momentum)*v....hence velocity of electron will be more that proton so...k.Eof electron will be more than proton...
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An electron and a proton have same de-Broglie's wavelength. The kineti...
Explanation:
The de Broglie wavelength for a particle is given by the equation:
λ = h / p
Where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.
Given:
An electron and a proton have the same de Broglie wavelength.
Analysis:
To find the kinetic energy of the electron, we can use the equation:
KE = (1/2) mv^2
Where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.
Since the de Broglie wavelength is the same for both the electron and the proton, we can equate their momentum:
p(electron) = p(proton)
Since momentum is given by the equation:
p = mv
We can rearrange the equation to solve for velocity:
v = p / m
Solution:
Step 1: Calculate the velocity of the electron and the proton using their respective masses and the de Broglie wavelength equation:
v(electron) = h / (λ * m(electron))
v(proton) = h / (λ * m(proton))
Step 2: Substitute the expressions for velocity in terms of momentum into the equation for kinetic energy:
KE(electron) = (1/2) m(electron) * (p(electron) / m(electron))^2
KE(proton) = (1/2) m(proton) * (p(proton) / m(proton))^2
Step 3: Since the de Broglie wavelength is the same for both the electron and the proton, we can equate their kinetic energy equations:
KE(electron) = KE(proton)
Conclusion: The kinetic energy of the electron is greater than that of the proton. Thus, the correct answer is option D.
The de Broglie wavelength for a particle is given by the equation:
λ = h / p
Where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.
Given:
An electron and a proton have the same de Broglie wavelength.
Analysis:
To find the kinetic energy of the electron, we can use the equation:
KE = (1/2) mv^2
Where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.
Since the de Broglie wavelength is the same for both the electron and the proton, we can equate their momentum:
p(electron) = p(proton)
Since momentum is given by the equation:
p = mv
We can rearrange the equation to solve for velocity:
v = p / m
Solution:
Step 1: Calculate the velocity of the electron and the proton using their respective masses and the de Broglie wavelength equation:
v(electron) = h / (λ * m(electron))
v(proton) = h / (λ * m(proton))
Step 2: Substitute the expressions for velocity in terms of momentum into the equation for kinetic energy:
KE(electron) = (1/2) m(electron) * (p(electron) / m(electron))^2
KE(proton) = (1/2) m(proton) * (p(proton) / m(proton))^2
Step 3: Since the de Broglie wavelength is the same for both the electron and the proton, we can equate their kinetic energy equations:
KE(electron) = KE(proton)
Conclusion: The kinetic energy of the electron is greater than that of the proton. Thus, the correct answer is option D.
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An electron and a proton have same de-Broglie's wavelength. The kinetic energy of an electron isa)infinityb)zeroc)equal to that of protond)greater than that of protonCorrect answer is 'D'. Can you explain this answer?
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