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**1. Homework Statement**

Consider a beta decay:

[tex]\ {X_Z^A} \rightarrow\ {Y_{Z+1}^A} \ + {\beta_{-1}^{0}}\ + {\bar\nu_e}[/tex]

To show that the KE of the recoil nucleus is

[tex]\ E = \frac{\ Q + \ 2 \ m \ c^2}{\ 2 \ M_Y \ c^2}\ {T_{max}}[/tex]

m and T(max) is the mass and maximum KE of beta particle

**2. Homework Equations**

**3. The Attempt at a Solution**

writing the expression for Energy conservation,we see that the electron rest energy terms cancels and the resulting equation is:

[tex]\ {T_y} + \ {T_\beta} + \ {T_{\bar\nu}}=\ Q = [ \ {M_x} - \ {M_y} - \ {M_{\beta}} - \ {M_{\bar\nu}} ] \ {c^2}[/tex]

For beta particle kinetic energy to be maximum, the kinetic energy of the neutrinos must be zero.(The kinetic energy of the recoiling nucleus assumed non-zero).

This gives an equation with known [tex]\ {T_y} + \ {T_\beta}[/tex]

But we need another equation to solve for the kinetic energy of Y.

I also used conservation of momentum---disregarding the momentum of the neutrinos.But that did not help.Can anyone please tell how to do it?

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