# Energy of Gamma ray = hf?

#### Ngineer

Hello everybody,

In one of my assignments I have lost a substanial portion of the grade for one problem because I haven't assumed that the energy of a Gamma ray = hf, I thought this was wrong, and that nothing in the statement says that it consists of only one photon. In fact, it says "high energy ray."

Does it make sense to you ? Should I make that assumption in the future? Should I talk to the prof about it?!

Thanks!

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#### gleem

The energy of an photon is hf. You would have had to use this info in the problem. From what you presented if you didn't use this then you should rework the problem.

#### Ngineer

I am not asking about the energy of a photon, I am asking about the energy of the gamma ray (which consists of a packet of photons).

#### Doc Al

Mentor
You need to realize that the interaction of the gamma "ray" is one photon at a time (the vast majority of the time).

#### Ngineer

I understand but the problem asks for the final mass of the atom, so in this case it is needed to know how many such collisions will take place.

#### Ngineer

Or to put it in question form, if we know that the atom loses x amu of mass per collision, how do we determine the final mass of the atom after the collision with "high energy ray" using only E=hf?!!

#### Doc Al

Mentor
I understand but the problem asks for the final mass of the atom, so in this case it is needed to know how many such collisions will take place.
You can safely assume that "a gamma ray" refers to a single photon collision.

#### Ngineer

Can you please elaborate on that assumption? Do all gamma rays consist of just one photon?

#### collinsmark

Homework Helper
Gold Member
Can you please elaborate on that assumption? Do all gamma rays consist of just one photon?
Usually when discussing "gamma ray" interactions with atoms, the "gamma ray" consists of an individual photon per interaction.

Even when dealing with lower energy light rays, if the question went something like, "an excited electron spontaneously falls to an intermediate energy state before falling to the ground state," the implication here is that there are two photons produced, one for each interaction of the electron changing states. Each individual interaction (of a charged particle, like an electron bound to an atom) involves a corresponding, single photon. [Edit: I suppose there might be situations where an atom releases a pair of entangled photons, but still, this has implications that greatly differ from a single photon at twice the energy. See below.]

In this problem it reads, "a high energy gamma ray with wavelength 1 nm is absorbed by atom 'X'. Immediately following this interaction [...]" The implication here is that there is a single photon related interaction, implying a single gamma ray photon is absorbed by the atom (exciting something or other within the atom), before a subsequent reaction takes place involving the x-ray (also a single photon) and the ejected electron.

Particularly when talking about high energy gamma rays, you should at least be prepared, when in doubt, to make the assumption that a "gamma ray" means a single, high energy photon.

As a matter of fact, that's pretty much the crux of quantum principles: Things happen in individual chunks. An atom absorbing a single photon of energy E might produce some interesting result (such as ejecting an electron and a lower energy photon). However, the interesting result would not happen if instead the atom simultaneously absorbed two photons of energy E/2, even though the total energy is the same. That's the fascinating result discovered by Albert Einstein in his 1905 paper on the photoelectric effect (one of a few of his groundbreaking papers published that year), which is also the origin of the E = hf equation.*

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All that said, the million dollar question: should you talk to your professor about it? I don't know. I'll leave that up to you. The implication is pretty strong in this case that the question here is talking about a single photon. However, if the question was something like, "a light ray strikes a refractive material with an index of refraction of 1.2. What is the angle of refraction?" that would not necessarily imply a single photon (however in that case there's no implication of a single, atomic-level event). If you got dinged pretty bad and you want to argue the case that you misunderstood the problem's single photon implication, you might get some credit back. Maybe. But I wouldn't hold your breath. It's up to you and your professor.

*[Edit: Although back in 1905, they were not called "photons." That term didn't come into use until much later. If I remember correctly, Einstein called them "corpuscles" or some such. The discrete packets of energy quality about them though was quite clear in his paper.]

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#### gleem

The terms gamma ray or x-ray always refers to a single photon as opposed to a light ray which referrers to a beam or stream of many photons. The term beam of x-rays would refer to many x-rays of unspecified number of individual x-rays each with energy hf. In any event interactions of photons either gamma, x-ray or light involve the interaction of a single photon of energy hf unless otherwise specified.

"Energy of Gamma ray = hf?"

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