Question

why can an electron not absorb the whole energy of a photon?

Answer 1

Hey friend,


here is your answer,

Can't believe I can't find a duplicate. It is because energy and momentum cannot be simultaneously conserved if a free electron were to absorb a photon. If the electron is bound to an atom then the atom itself is able to act as a third body repository of energy and momentum.

Details below:

Conservation of momentum when a photon (νν) interacts with a free electron, assuming that it were absorbed, gives us

p1+pν=p2,(1)(1)p1+pν=p2,

where p1p1 and p2p2 are the momentum of the electron before and after the interaction. Conservation of energy gives us

(p21c2+m2ec4)−−−−−−−−−−−√+pνc=(p22c2+m2ec4)−−−−−−−−−−−√(2)(2)(p12c2+me2c4)+pνc=(p22c2+me2c4)

Squaring equation (2) and substituting for pνpν from equation (1), we have

p21c2+m2ec4+2(p2−p1)(p21c2+m2ec4)−−−−−−−−−−−√+(p2−p1)2c2=p22c2+m2ec4p12c2+me2c4+2(p2−p1)(p12c2+me2c4)+(p2−p1)2c2=p22c2+me2c4

(p2−p1)2c2−(p22−p21)c2+2(p2−p1)c(p21c2+m2ec4)−−−−−−−−−−−√=0(p2−p1)2c2−(p22−p12)c2+2(p2−p1)c(p12c2+me2c4)=0

Clearly p2−p1=0p2−p1=0 is a solution to this equation, but cannot be possible if the photon has non-zero momentum. Dividing through by this solution we are left with

(p21c2+m2ec4)−−−−−−−−−−−√−p1c=0(p12c2+me2c4)−p1c=0

This solution is also impossible if the electron has non-zero rest mass (which it does). We conclude therefore that a free electron cannot absorb a photon because energy and momentum cannot simultaneously be conserved.





hope helps for u

Answer 2

The premise of this question is actually false. First, I'll need to rewrite it slightly. "Partial absorption" of a photon doesn't make sense. Photons are particles - you can have 0 photons or 1 photon but not half a photon. But you can change this is "Partial absorption of the photon's energy" and then it is kosher. So, the modified question reads

"Why does a photon transfer all its energy to an electron (and disappears) rather than transferring part of its energy and continuing to exist?"

The premise is untrue - the photon CAN transfer part of its energy to the electron and continue to exist. An example of this is Compton scattering, where a gamma ray (a type of photon) transfers enough energy to the electron to ionize and move it out of the atom's potential well.

On the other end of the spectrum, consider the passage of light through a transparent material. Here the light scatters off the electrons in the material elastically (in a way that transfers no energy to the electrons). So the photons interact with the electrons and transfer NO energy. There are also types of elastic scattering such as Rayleigh scattering which I don't know enough about to describe.

Often the process you describe happens, where the photon is completely absorbed by the electron. This is an electron that is trapped by the atom and can only exist in certain energy levels. This is not because energy is quantized, as César Tomé-López says (perhaps I misunderstood him). Any energy is possible in principle - just not in the atom. The quantization is because of the nature of the Coulomb force coupling the electron to the nucleus.

So, you might ask, why can't the photon transfer part of its energy to the electron (enough to transition between two energy levels) and then travel on with reduced energy? After all, it can transfer enough energy to completely ionize the electron, why not just enough to excite the electron between two energy states? I don't think this is a simple question, or if it is I do not know its simple answer. I think it might be due to conservation of angular momentum.

Another possibility is the intricacy of a photon scattering event. Although I have talked as though the photon and electron simply exchange energy, what actually happens is that the photon and electron join into a higher energy electron that then reemits a photon. Perhaps this intermediate electron is forced to exist in one of the quantized energy levels. I am unsure about this, because generally these intermediate virtual particles can do crazy things like violate energy conservation for a brief period of time.