Linear momenta of a proton and an electron are equal. Relative to an e...
If p
e = p
p,
therefore, de-Broglie wavelength of proton and electron are equal.
The correct answer is: de-Broglie wavelength of proton and electron are equal
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Linear momenta of a proton and an electron are equal. Relative to an e...
Relative to an electron, the linear momenta of a proton and an electron are equal. This means that the magnitude of the momentum of the proton is the same as that of the electron, but their directions are opposite.
Explanation:
The linear momentum (p) of a particle is given by the product of its mass (m) and velocity (v): p = mv.
Given that the linear momenta of the proton and electron are equal, we can write:
mpvp = meve,
where mp and me are the masses of the proton and electron respectively, and vp and ve are their velocities.
Now, let's consider the de Broglie wavelength for the proton and electron.
The de Broglie wavelength (λ) of a particle is given by the ratio of its Planck's constant (h) to its momentum: λ = h/p.
For the proton, the de Broglie wavelength is given by λp = h/mpvp.
For the electron, the de Broglie wavelength is given by λe = h/meve.
Since mpvp = meve, we can see that the de Broglie wavelengths of the proton and electron are equal: λp = λe.
Therefore, the correct answer is option C: the de Broglie wavelength of the proton and electron are equal.
This result is consistent with the wave-particle duality of quantum mechanics, which states that particles can exhibit both wave-like and particle-like properties. The de Broglie wavelength is a measure of the wave-like nature of a particle, and in this case, it is the same for both the proton and electron.
Linear momenta of a proton and an electron are equal. Relative to an e...
If p
e = p
p,
therefore, de-Broglie wavelength of proton and electron are equal.
The correct answer is: de-Broglie wavelength of proton and electron are equal