An electron and a proton posses the same de broglie wavelength. If Ee ...
(a) v/c
for kinetic energy E, Momentum P, Mp is mass of proton and Me is mass of electron ,Vp is speed of proton
for same De Broglie wavelength Lambda,
lambda =h/√(2mE)
So Ee×Me=Ep×Mp--------------(1)
also Lambda =h/mv
So
Me/Mp= Vp/Ve
Me/Mp=c/v ----------------------(2)
Solving (1)&(2) we get,
Ee/Ep=v/c
An electron and a proton posses the same de broglie wavelength. If Ee ...
De Broglie Wavelength and Energy
The De Broglie wavelength, denoted by λ, is a concept in quantum mechanics that relates the momentum and wavelength of a particle. It is given by the equation:
λ = h / p
where λ is the De Broglie wavelength, h is the Planck's constant, and p is the momentum of the particle.
The momentum of a particle can be calculated as:
p = mv
where m is the mass of the particle and v is its velocity.
Equal De Broglie Wavelengths
Given that the electron and proton possess the same De Broglie wavelength, we can equate their momentum equations:
melectron * velectron = mproton * vproton
where melectron and mproton are the masses of the electron and proton respectively, and velectron and vproton are their velocities.
Comparing Energies
The energy of a particle can be calculated using the equation:
E = mc^2
where E is the energy, m is the mass of the particle, and c is the speed of light.
For the electron, we have:
Ee = melectron * c^2
For the proton, we have:
Ep = mproton * c^2
To compare the energies, we can calculate the ratio:
Ee / Ep = (melectron * c^2) / (mproton * c^2)
Simplifying the equation, we find:
Ee / Ep = melectron / mproton
Ratio of Electron and Proton Energies
Since the electron and proton possess the same De Broglie wavelength, their momentum equation can be rearranged as:
velectron / vproton = mproton / melectron
Substituting this into the ratio of energies equation, we get:
Ee / Ep = melectron / mproton = velectron / vproton
Therefore, the ratio of the electron energy to the proton energy is equal to the ratio of their velocities:
Ee / Ep = velectron / vproton
Answer
Therefore, the correct answer is (a) v / c. The ratio of the electron energy to the proton energy is equal to the ratio of their velocities, which is v / c.
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