Question

The moving electron and a photon has same de Broglie wavelength. Show that the electron possesses more energy than carried by the photon.

Answer 1

we know that both are having same momentum and energy is p^2/2m mass of e is less than proton so electron posses more energy

Answer 2

heya...

Here is your answer..

If a photon and electron have the same de Broglie wavelength, which has the greater total energy?

Answer

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9 ANSWERS



Ashok Narayan, former Retired From Indian Administrative Service at Government of Gujarat, India (1966-2004)

Answered Feb 27

Let us consider an electron and a photon of the same de Broglie wavelength λ

Total Energy

Let the electron have a relativistic mass m

Then its momentum =mv = h/ λ, so m= h/ λv… (1)

Momentum of the photon is also h/ λ, so its effective mass mγ =h/λc…(2)

Since v<c, m> mγ

Since, E (the total energy) =Relativistic mass* c2, it follows that the total energy of the electron is greater than that of the photon, both having the same wavelength.

Kinetic Energy (KE)

In the case of the photon, all its energy is kinetic, which is ch/ λ. This can also be written as p2/ =mγ, where E= KE = pc

For the electron, KE = p2/2m

Thus KE (photon)/KE (electron) =2m/ mγ =2c/v (from (1) and (2), which is >1 (since c>v))

Therefore, KE of the photon (which is also the total energy of the photon) is greater than the kinetic energy of the electron, both having the same wavelength.

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