# What Is the Laboratory Energy of a Proton Given Photon Energy Shifts?

• cartonn30gel
In summary, in the given scenario, the energy of a photon in the frame of reference of a laboratory is 35eV, while in the frame of reference of a proton, it is 5MeV. Using the relativistic doppler effect and Lorenz velocity transformations, it can be determined that the proton is approaching the photon at a speed just slightly less than the speed of light. This results in a massive amount of energy for the proton, but not infinite, as objects with mass cannot reach the speed of light.
cartonn30gel
1. Homework Statement

We are in a laboratory and there is a photon and an ultra-relativistic proton moving. The energy of the photon in the frame of reference of the laboratory is 35eV. The energy of the same photon in the frame of reference of the proton is 5MeV. What is the energy of the proton in the frame of reference of the laboratory?

2. Homework Equations

energy = h*f
Relativistic doppler effect
Lorenz velocity transformations
relativistic energy

3. The Attempt at a Solution

using energy = h*f

first frequency (f1) is 8.48*10^(15) Hz
second frequency (f2) is 1.21*10^(21) Hz

change of frequency is I guess because of Doppler effect
because f2 > f1, the proton and the photon must be approaching each other. But no matter what, the proton will see the photon approaching with a speed of c. I am not sure if it is valid to use the Doppler formula here. If I use, I get,
B=v/c=0,99999 (the relative speed of the photon and the proton)

then using Lorenz velocity transformation in x direction I get the speed of the proton to be -c. I thought this could be an indication of the proton's actually to be moving away from the photon (that means both moving in the same direction)

But then I cannot use Energy= (gama)*m*c^(2) because (gama) will be infinite.

I'd appreciate any help.
thanks

Well I posted this response on your topic in intro physics before I noticed you moved it, here it is again in case you didn't see

I believe you're right to use the doppler effect, but I didn't follow your application

The relativistic doppler shift is frequency observed = sqrt[(1-v/c)/(1+v/c)]*frequency emitted from the source

The problem is V is going to be humongous and yes, negative

f2/f1 is like somethingx10^35, so you get (10^35-1)=-(10^35+1)v/c

Divide both sides by 10^35+1 and you get -v/c=a number just so very much almost 1 but just not quite, like .9999 out to 30+ decimal places

Now when you use the equation like I did, you're assuming positive V means they're moving AWAY from each other, so the negative means the opposite of what you concluded, they're rushing towards each other, and the proton is basically going an incredibly small amount less than c. So yes gamma is going to be gigantic to the point of ludicrous and the energy of the proton is going to be gigantic to the point of unreasonable. But I think that's the idea

If it were ACTUALLY going the speed of light, which you rounded off too, then yes it would have infinite energy.

Which is the point, objects with mass don't get to go the speed of light because we can't impart infinite energy to them. So I think you did the problem right, me following or not, but reached the wrong conclusion

## 1. How is the speed of a proton measured?

The speed of a proton is measured using a device called a particle accelerator. This device uses electric and magnetic fields to accelerate protons to very high speeds, which can then be measured using specialized detectors.

## 2. What is the fastest speed a proton can reach?

The fastest speed a proton can reach is the speed of light, which is approximately 299,792,458 meters per second. However, in practical applications, protons can be accelerated to speeds close to the speed of light but not quite reaching it.

## 3. How does the speed of a proton compare to other particles?

The speed of a proton is relatively slow compared to other particles, such as electrons or neutrinos. However, protons are still very fast and can reach speeds close to the speed of light when accelerated in a particle accelerator.

## 4. Can the speed of a proton change?

Yes, the speed of a proton can change depending on the environment it is in. In a vacuum, protons can travel at very high speeds, but in a medium such as air or water, they will slow down due to interactions with other particles.

## 5. Why is the speed of a proton important in scientific research?

The speed of a proton is important in scientific research because it allows scientists to study the behavior and properties of particles at high energies. This is crucial in fields such as particle physics, where understanding the behavior of protons at high speeds can provide insights into the fundamental nature of matter and the universe.

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