Question

7. A neutron at rest decays (breaks apart) into a proton and an electron. Energy is released in the decay, in the form of kinetic energy of the proton and electron. The mass of a proton is 1836 times the mass of an electron. What fraction of the total energy released goes into the kinetic energy of the proton?

Answer 1

Answer:

The fraction of the total energy goes into kinetic energy of proton is $5.44 \times 10^{-4}$

Explanation:

Given:

Mass of proton $m_{p} = 1836 m_{e}$

Mass of electron $m_{e} = 9.1 \times 10^{-31}$ kg

Here neutron at rest decays into proton and electron

   $n_{1} ^{0}$  ⇄ $P_{1} ^{1} + e_{0} ^{-1} + Q$

Where $Q =$ energy released

The $Q$ value of this reaction is given by

    $Q = (\frac{m_{p} +m _{e} }{m_{e} } ) K$

Where $K =$ kinetic energy of reaction

Here we need to find fraction of the total energy released goes into the kinetic energy of the proton

   $\frac{K}{Q} = \frac{m_{e} }{m_{p} + m_{e} }$

   $\frac{K}{Q} = (\frac{m_{e} }{1836m_{e} + m_{e} } )$

   $\frac{K}{Q} = \frac{1}{1837}$

   $\frac{K}{Q} = 5.44 \times 10^{-4}$

Therefore, the fraction of the total energy goes into kinetic energy of proton is $5.44 \times 10^{-4}$