Answer:
42.84
Explanation:
Let's take [tex]v_p[/tex] to be the proton's velocity and [tex]v_e[/tex] to be the electron's velocity and [tex]V[/tex] to be the potential difference through which both the charges are accelerated and further taking [tex]e[/tex] be the charge of proton and electron.
Using the given values:
[tex]m_p=1.67\times10^-^2^7kg\\\\m_e=9.1\times 10^{-31}kg[/tex]
The expression for the work done is
[tex]W_p=W_e=eV[/tex]
Solving for the kinetic energy equation:
[tex]W_p=W_e\\\\0.5m_pv_p^2=0.5m_ev_e^2\\\\\frac{v_e}{v_p}=\sqrt{\frac{m_p}{m_e}}\\\\=\sqrt{\frac{1.67\times10^{-27}}{9.1\times10^{-31}}}\\\\=42.83[/tex]
Thus the ratio ve/vp. ve/vp =42.84
