Question

An electron and a proton, starting from rest, are accelerated through an electric potential difference of the same magnitude. In the process, the electron acquires a speed ve, while the proton acquires a speed vp. Find the ratio ve/vp. ve/vp =

Answer 1

Answer:

42.84

Explanation:

Let's take $v_p$ to be the proton's velocity and $v_e$ to be the electron's velocity and $V$ to be the potential difference through which both the charges are accelerated  and further taking $e$  be the charge of proton and electron.

Using the given values:

$m_p=1.67\times10^-^2^7kg\\\\m_e=9.1\times 10^{-31}kg$

The expression for the work done is

$W_p=W_e=eV$

Solving for the kinetic energy equation:

$W_p=W_e\\\\0.5m_pv_p^2=0.5m_ev_e^2\\\\\frac{v_e}{v_p}=\sqrt{\frac{m_p}{m_e}}\\\\=\sqrt{\frac{1.67\times10^{-27}}{9.1\times10^{-31}}}\\\\=42.83$

Thus the  ratio ve/vp. ve/vp =42.84