Respuesta :
Answer:
The fraction of the total energy goes into kinetic energy of proton is [tex]5.44 \times 10^{-4}[/tex]
Explanation:
Given:
Mass of proton [tex]m_{p} = 1836 m_{e}[/tex]
Mass of electron [tex]m_{e} = 9.1 \times 10^{-31}[/tex] kg
Here neutron at rest decays into proton and electron
[tex]n_{1} ^{0}[/tex] ⇄ [tex]P_{1} ^{1} + e_{0} ^{-1} + Q[/tex]
Where [tex]Q =[/tex] energy released
The [tex]Q[/tex] value of this reaction is given by
[tex]Q = (\frac{m_{p} +m _{e} }{m_{e} } ) K[/tex]
Where [tex]K =[/tex] kinetic energy of reaction
Here we need to find fraction of the total energy released goes into the kinetic energy of the proton
[tex]\frac{K}{Q} = \frac{m_{e} }{m_{p} + m_{e} }[/tex]
[tex]\frac{K}{Q} = (\frac{m_{e} }{1836m_{e} + m_{e} } )[/tex]
[tex]\frac{K}{Q} = \frac{1}{1837}[/tex]
[tex]\frac{K}{Q} = 5.44 \times 10^{-4}[/tex]
Therefore, the fraction of the total energy goes into kinetic energy of proton is [tex]5.44 \times 10^{-4}[/tex]
