# End Point Energy and Q value in beta decay

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## Main Question or Discussion Point

I know that Q value of a reaction is the difference between total initial mass-energy and total final mass-energy of all the products. Then shouldn't be this also the maximum kinetic energy and hence endpoint energy of an electron in beta decay. But what I have read endpoint energy ##E_0 = Q + m_e c^2 ## where ##m_e## is the rest mass of electron. I'm thinking ##Q=E_0##. What I'm thinking wrong? #### Attachments

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Orodruin
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I have edited the question and attached the lecture slide I am reading.

I think I'm getting confused about the definition of endpoint energy. Is it the maximum kinetic energy of electron observed or the total relativistic energy of the beta particle.

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Orodruin
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This is still not a proper reference. Please refer to somewhere where we can check the entire source material.

If you let a particle of mass ##M## decay at rest in a two-body decay with product masses ##\mu## and ##m## with ##m < \mu < M## (which is essentially what you have for the beta decay if you look at the endpoint energy and ignore the neutrino mass), the resulting kinetic energy of the particle of mass ##m## will be
$$T = Q\left( 1 - \frac{Q+2m}{2M}\right),$$
where ##Q = M - \mu - m## (assuming I did the algebra correctly, this is a basic particle kinematics exercise). For ##Q,m \ll M## this expression becomes ##T \simeq Q##.

This is still not a proper reference. Please refer to somewhere where we can check the entire source material.

If you let a particle of mass ##M## decay at rest in a two-body decay with product masses ##\mu## and ##m## with ##m < \mu < M## (which is essentially what you have for the beta decay if you look at the endpoint energy and ignore the neutrino mass), the resulting kinetic energy of the particle of mass ##m## will be
$$T = Q\left( 1 - \frac{Q+2m}{2M}\right),$$
where ##Q = M - \mu - m## (assuming I did the algebra correctly, this is a basic particle kinematics exercise). For ##Q,m \ll M## this expression becomes ##T \simeq Q##.
Okay, but can you define exactly what endpoint energy is. In the article: https://www.nucleonica.com/wiki/index.php?title=Endpoint_energy, it says ##E_0 = Q + m_e c^2## which is "mass difference between the parent and daughter nuclides" for beta decay. So endpoint energy is not the maximum kinetic energy observed in an experiment but maximum kinetic energy + rest mass energy?

Orodruin
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So endpoint energy is not the maximum kinetic energy observed in an experiment but maximum kinetic energy + rest mass energy?
That would be maximal total energy of the electron. You should make it clear which energy you refer to.

• avkr
That would be maximal total energy of the electron. You should make it clear which energy you refer to.
got it. thanks!