How Is the Total Energy of Photons Calculated in Electron-Positron Collisions?

In summary, when a positron and an electron collide head on, the total energy of the two resulting photons can be calculated by using the equations E=mc^2 and E=γmc^2, where γ is the Lorentz factor calculated from the particles' speeds. The final formula for the total energy of the two photons is 2(RE + KE + PE + Mass), where RE is the rest energy of one particle, KE is the kinetic energy of one particle, PE is the potential energy of the system, and Mass is the total mass of the particles.
  • #1
magma_saber
73
0

Homework Statement


Suppose that a positron traveling at a speed of 0.93c collides head on with an electron traveling at the same speed.

What is the sum of the energies of the two photons?


Homework Equations


mass of an electron = 9e-31 kg
E=[tex]\gamma[/tex]mc2 - mc2


The Attempt at a Solution


2.2032e-13 - 8.1e-14 = 1.3932e-13
1.393e-13 * 2 = 2.7864e-13 J
 
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  • #2
I have a few comments:

It's kind of hard to follow what you are doing. Including units with all values in your equations would help with that.

I don't see where or if you have calculated γ.

Also, it's probably easier to work in eV energy units, rather than Joules. Your textbook might even give the value of mc2 for the electron, in eV units.
 
  • #3
the questions ask for in Joules.

rest energy = mc2
(9e-31)*(3d8)2 = 8.1e-14

[tex]\gamma[/tex] = 1/[tex]\sqrt{1-(0.93)^2}[/tex] = 2.72

particle energy = [tex]\gamma[/tex]*mc2
(2.72)*(9e-31)*(3d8)2 = 2.20e-13

E = particle energy - rest energy
E = 2.20e-13 - 8.1e-14 = 1.39e-13

Then i multiplied it by 2 since that is the energy of one of the particle.
1.39e-13*2 = 2.79e-13 J
 
  • #4
magma_saber said:
the questions ask for in Joules.
Okay, understood.

rest energy = mc2
(9e-31)*(3d8)2 = 8.1e-14

[tex]\gamma[/tex] = 1/[tex]\sqrt{1-(0.93)^2}[/tex] = 2.72

particle energy = [tex]\gamma[/tex]*mc2
(2.72)*(9e-31)*(3d8)2 = 2.20e-13
Looks good.
E = particle energy - rest energy
E = 2.20e-13 - 8.1e-14 = 1.39e-13
Here E is the kinetic energy of one of the particles. However, it is the total particle energy, kinetic and rest mass, that ultimately is converted into the photons.

Then i multiplied it by 2 since that is the energy of one of the particle.
Yes, but you'll need to use the total energy rather than only kinetic. Looks good otherwise.
 
  • #5
Redbelly98 said:
Okay, understood.Looks good.

Here E is the kinetic energy of one of the particles. However, it is the total particle energy, kinetic and rest mass, that ultimately is converted into the photons.Yes, but you'll need to use the total energy rather than only kinetic. Looks good otherwise.

I have a similar problem and I followed the posters procedure but I am however confused as to why we need to add rest mass as the instructor has said. If someone would clarify this problem in better detail much appreciated.

I am just confused, is the final formula:
2(RE + KE + PE + Mass) = Total Energy of the two photons?
 

Related to How Is the Total Energy of Photons Calculated in Electron-Positron Collisions?

What is the concept of "Sum of photon energies"?

The "sum of photon energies" refers to the total amount of energy carried by a group of photons. Photons are packets of energy that make up electromagnetic radiation, and their individual energies can be added together to determine the total energy of the group.

How is the sum of photon energies calculated?

The sum of photon energies is calculated by multiplying the number of photons by the energy of each individual photon. This is commonly represented by the equation E = nhν, where E is the total energy, n is the number of photons, and hν is the energy of each photon.

What is the relationship between frequency and energy of photons?

The energy of a photon is directly proportional to its frequency. This means that as the frequency of a photon increases, its energy also increases. This relationship is described by the equation E = hν, where E is the energy and ν is the frequency.

Can the sum of photon energies be negative?

No, the sum of photon energies cannot be negative. Photons always carry a positive amount of energy, and when added together, the result will always be a positive value. Negative energies are not possible in the context of photons.

How is the concept of "Sum of photon energies" relevant in scientific research?

The concept of "sum of photon energies" is relevant in many areas of scientific research, particularly in the fields of quantum mechanics and spectroscopy. It is used to calculate the total energy of a system and can provide valuable insights into the behavior and properties of different materials and molecules.

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