How to relate mass defect to kinetic energies?

In summary, the conversation discusses a nuclear question related to the Q-factor and kinetic energy of parent particles during a decay process. The equations for Q are true in the rest frame of the parent particle and relate to the rest masses of the particles. The question might be asking for the relationship between Q and the rest masses in a decay process.
  • #1
rwooduk
762
59

Homework Statement


Just one more nuclear question if I may,

wrG9UEO.jpg


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)

aIH3YsV.jpg


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.
 
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  • #2
rwooduk said:
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.
 
  • #3
mfb said:
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
 
  • #4
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?
 
  • #5
mfb said:
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?
 
  • #6
Particle decay is always a process of a single particle (can be composite like a hadron, but then it is still a single object).
 
  • #7
mfb said:
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?
 
  • #8
Probably.
 
  • Like
Likes rwooduk

1. What is the definition of mass defect in relation to kinetic energies?

Mass defect is the difference between the mass of an atom's nucleus and the sum of the masses of its individual protons and neutrons. This loss of mass is converted into kinetic energy during nuclear reactions.

2. How is mass defect calculated and measured?

Mass defect is calculated by subtracting the mass of the individual protons and neutrons of an atom from the mass of its nucleus. It is measured in atomic mass units (amu) or in kilograms (kg) using the equation E=mc^2, where E is the energy, m is the mass defect, and c is the speed of light.

3. What is the significance of mass defect in nuclear reactions?

Mass defect plays a crucial role in nuclear reactions as it is responsible for the release of large amounts of energy. This energy is harnessed to power nuclear reactors and can also be used in nuclear weapons.

4. How does mass defect relate to the binding energy of atoms?

Mass defect is directly related to the binding energy of atoms. The more energy that is required to hold the nucleus together, the greater the mass defect will be and vice versa. This is known as the mass-energy equivalence principle.

5. What is the practical application of understanding the relationship between mass defect and kinetic energies?

Understanding the relationship between mass defect and kinetic energies is essential in the development of nuclear power and weapons. It also has applications in medical imaging and cancer treatment, as well as in the study of the origins of the universe through nuclear reactions.

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