How to relate mass defect to kinetic energies?

[rwooduk]

Homework Statement

Just one more nuclear question if I may,

Homework Equations

None.

The Attempt at a Solution

I can do the first part of this question, but am unsure on the second part. I thought it may be related to the Q-factor (the difference in energy of the initial and final products for a reaction) but I'm not sure. And how can the parent products have kinetic energy? is it moving?

Does it relate to this diagram (sorry for the quality, my paint skills have decayed exponentially since my teenage years)

Or am I right in thinking it wants the Q-factor equation which would be somethihng like $Q = M_{parent} - M_{daughter}> 0\\\\ Q= \sum E_{k}$

thanks again for any ideas.

 

[mfb]

And how can the parent products have kinetic energy? is it moving?

There are always frames where the parent particle is moving.
What are P_min and P_max?
Those equations for Q are true in the rest frame of the parent particle only.

 

[rwooduk]

There are always frames where the parent particle is moving.
What are P_min and P_max?
Those equations for Q are true in the rest frame of the parent particle only.

P_min and P_max relate to the graph for beta decay wiht intensity vs momentum, and describe how the particles have different directions for min and max. I'm unsure if it's related.

What do you think the question is trying to get at?

thanks again for the reply

 

[mfb]

In the rest frame, you know the sum of kinetic energies is always the same (it is Q).
How is Q related to the rest masses of the particles?

 

[rwooduk]

In the rest frame, you know the sum of kinetic energies is always the same (it is Q).
How is Q related to the rest masses of the particles?

If you had 2 particles decaying into 2 other particles it would be

$Q=\Delta mc ^{2}=(m_{A}+m_{B})c^{2}-(m_{C}+m_{D})c^{2}= E_{Kin,C}+ E_{Kin,D}-E_{Kin,A}-E_{Kin,B}$

hmm have I just answered the question?

 

[mfb]

Particle decay is always a process of a single particle (can be composite like a hadron, but then it is still a single object).

 

[rwooduk]

Particle decay is always a process of a single particle (can be composite like a hadron, but then it is still a single object).

Good point, I'm not sure why that is given in the notes, perhaps just an example of what Q is.

So

$Q=\Delta mc ^{2}=E_{Kin,A}-E_{Kin,B}-E_{Kin,C}$ where A is the decaying particle and B and C are the products, would you think that would be what the question is asking for?

 

[mfb]

Probably.