Nuclear Photo Reaction + Threshold Energy

[spekky_bandit]

Homework Statement

I am given a scenario where a photon and a nuclei interact and create two daughter nuclei/particles. I won't bother with the full scenario as it would be nice to solve this generally, but we may assume we know the mass of all nuclei involved.

The question is then what is the threshold energy for the photon for this reaction to occur, assuming that the Q value is negative and known, and that the parent nuclei starts at rest?

Homework Equations

Conservation of momentum and energy (we assume non-relativistic at least for now)

The Attempt at a Solution

So I know that essentially I want to conserve both energy and momentum to work out the kinetic energy of both of the daughter nuclei. This result - the Q value would then be the required photon threshold energy. The problem arises in that I can't find solutions for the daughter kinetic energies in terms of the photon energy without introducing daughter nuclei velocities to my equations, essentially providing more unknown variables.

A few hints would be greatly appreciated.

Cheers

 

[mark726]

it is important to approach a problem by first understanding the concepts involved and then applying the appropriate equations. In this scenario, we are dealing with the interaction of a photon and a nuclei, resulting in the creation of two daughter nuclei/particles. The key concept to understand here is the conservation of energy and momentum.

To solve this problem, we can start by writing down the conservation of energy and momentum equations. Since the parent nuclei is at rest, the initial momentum is zero. Therefore, we can write the conservation of momentum equation as:

pγ = p1 + p2

Where pγ is the momentum of the photon and p1 and p2 are the momentums of the two daughter nuclei.

Next, we can write the conservation of energy equation as:

Eγ = E1 + E2 + Q

Where Eγ is the energy of the photon, E1 and E2 are the energies of the two daughter nuclei, and Q is the Q value of the reaction.

Now, we can solve for the kinetic energy of the daughter nuclei by using the equation:

K1 = E1 - m1c^2

Where K1 is the kinetic energy of the first daughter nuclei, E1 is the energy of the first daughter nuclei, and m1 is the mass of the first daughter nuclei. Similarly, we can find the kinetic energy of the second daughter nuclei using the equation:

K2 = E2 - m2c^2

Where K2 is the kinetic energy of the second daughter nuclei, E2 is the energy of the second daughter nuclei, and m2 is the mass of the second daughter nuclei.

Now, we can substitute these equations into the conservation of energy equation and solve for the photon energy:

Eγ = K1 + K2 + m1c^2 + m2c^2 + Q

Finally, we can solve for the threshold energy of the photon by setting the Q value to be negative and known, and solving for Eγ. This will give us the minimum energy that the photon must have for the reaction to occur.

In summary, to solve this problem, we used the conservation of energy and momentum equations and the concept of kinetic energy to solve for the threshold energy of the photon. It is important to understand the concepts involved and then apply the appropriate equations to solve the problem.