# Solving Nuclear Problem: Minimum Photon Energy

• matt222
In summary: If the speeds are nonrelativistic you'll need to use the nonrelativistic formulas. If you don't know what formulas to use, you might want to look in a textbook or notes or something, to see if you can find them. If you do have them, then you should be able to work through the problem yourself.In summary, the problem is to find the minimum photon energy needed to produce a proton and neutron from a gamma ray interacting with a deuteron. Two cases are being considered; in the first case, the proton and neutron both acquire equal, collinear velocities, while in the second case the neutron stays at rest after the collision. Finally, the question is raised as to why

#### matt222

Nuclear problem,,,

A Gamma photon is used in order to dissociate deuterium into a proton and neutron. the binding energy is 2.22Mev anf the rest energies for the proton and neutron are 938Mev and 939Mev respectively. determine the minmum photon energy to achieve this. consider two cases:
1- both proton and neutron acquire collinear equal velocities parallel to the photon Momentum
2-the neutron stays staionary after the collission
3- why non-collinear not considered in this analysis

Binding energy= (total number of proton and neutron)- minimum photon energy

2.22=939+938-E(MINIMUM)

E(MINIMUM)=1874.78Mev

for part 2:

since the neutron is stationary so this mean we have a zero energy for neutron and we will left only with proton energy and the minimum photon energy in this case would be:

E(MINIMUM)=939-2.22=936.78Mev

for part 3:

for non-collinear this is because the momentum is not conserved

what do you think guys i am doing well

matt222 said:
A Gamma photon is used in order to dissociate deuterium into a proton and neutron. the binding energy is 2.22Mev anf the rest energies for the proton and neutron are 938Mev and 939Mev respectively. determine the minmum photon energy to achieve this. consider two cases:
1- both proton and neutron acquire collinear equal velocities parallel to the photon Momentum
2-the neutron stays staionary after the collission
3- why non-collinear not considered in this analysis

Binding energy= (total number of proton and neutron)- minimum photon energy

2.22=939+938-E(MINIMUM)

E(MINIMUM)=1874.78Mev

No, you are doing as if the neutron and proton were remaining at rest. You must take into account that they must move so you must consider both conservation of energy and of momentum. In addition, you don't take into account that the proton and neutron's rest mass energies are there both before and after the interaction! So it's completely off.
Write the total energy before and after. Write the total momentum before and after
i

Energy before colission is and after collsion is:

m1v1/2+m2v2/2=m1u1/2+m1u2/2

total momentum:

m1v1+m2v2=m1u1+m2u2

so if both proton and neautron have equal velocities so total energy would equal to:

m1+m2=m1+m2

was that true

Hi matt222,

I replied to another thread from you with this same problem about 5 days ago; did you not see it? It was at:

My post there indicated that your binding energy formula was wrong; the 2.22 MeV in this problem is the difference between the rest mass of the proton and neutron when they are separated and when they are combined.

In the last post in this thread, you have written down some energy and momentum conservation conditions for nonrelativistic speeds. That's the right procedure to follow, however, I think there are two problems: First, you have neglected the photon's momentum and energy. For example, the momentum that the proton and neutron have after the collision is equal to the momentum that the photon had before the collision.

Second, I think the speeds involved are relativistic speeds; if that's true you'll need the relativistic energy and momentum formulas.

## 1. What is the minimum photon energy needed to solve the nuclear problem?

The minimum photon energy needed to solve the nuclear problem varies depending on the specific problem being addressed. However, in general, a high enough energy is needed to overcome the strong nuclear force that binds the nucleus together. This energy is typically in the range of millions to billions of electron volts (MeV to GeV).

## 2. How is the minimum photon energy calculated?

The minimum photon energy is calculated by considering the specific nuclear reaction or process being studied. This involves taking into account factors such as the mass and charge of the particles involved, the energy required to overcome the strong nuclear force, and any other relevant physical parameters.

## 3. What are some techniques used to generate high-energy photons for solving the nuclear problem?

Some techniques used to generate high-energy photons for solving the nuclear problem include particle accelerators, synchrotron radiation facilities, and laser-plasma interactions. These methods can produce photons with energies in the MeV to GeV range, allowing for the study of nuclear reactions and processes.

## 4. Why is it important to determine the minimum photon energy for solving the nuclear problem?

Determining the minimum photon energy needed for solving the nuclear problem is crucial for understanding the fundamental processes that govern the behavior of atomic nuclei. It also has practical applications, such as in nuclear energy production and medical imaging techniques.

## 5. Are there any challenges in solving the nuclear problem with high-energy photons?

Yes, there are several challenges in solving the nuclear problem with high-energy photons. These include the difficulty in generating and controlling high-energy photons, as well as the complexity of nuclear reactions and processes. Additionally, there are safety concerns and ethical considerations when working with high-energy particles.