Answer:
[tex]5.44\times 10^-^4[/tex]
Explanation:
Let [tex]A[/tex] and [tex]B[/tex] represent proton and electron respectively
Total energy decay is:
[tex]Q=K_A+K_B[/tex] (1)
where [tex]K=\frac{1}{2} mv^2[/tex] (2)
The momentum of the particle is given by:
[tex]\overrightarrow{p}=m\overrightarrow{v}[/tex]
After the decay we have [tex]\overrightarrow{p}_A+ \overrightarrow{p}_B=0[/tex] (3)
Since the particles move in opposite direction,
[tex]\overrightarrow{p}_A=m_Av_A, \overrightarrow{p}_B=-m_Bv_B[/tex]
From eq (3) we get [tex]m_Av_A=m_Bv_B, v_B=v_A\frac{m_A}{m_B}[/tex] (4)
From eq (2) we get [tex]K_B=\frac{1}{2} mv_B^2[/tex]
From eq (1) and (4), [tex]Q=K_A+\frac{1}{2}m_B(v_A \frac{m_A}{m_B})^2[/tex]
[tex]Q=K_A+\frac{1}{2}m_Av_A^2 (\frac{m_A}{m_B})[/tex]
[tex]K_A=\frac{1}{2}m_Av_A^2,Q=K_A+K_A(\frac{m_A}{m_B})=K_A(1+\frac{m_A}{m_B})[/tex]
[tex]m_A=1836m_B ,Q=K_A(1+1836)[/tex]
[tex]\frac{K_A}{Q}=\frac{1}{1837}=5.44\times 10^-^4[/tex]
