Question

An α - particle and a proton are accelerated through same potential difference. Find the ratio (Vα/ Vp)of velocities acquired by two particles.

Answer 1

Answer:

The ratio (Vα/ Vp)of velocities acquired by two particles is

$\frac{v_{\alpha}}{v_p} = \sqrt{\frac{1}{2}}$

Explanation:

As we know that when charge particle is accelerated by a given potential difference then the kinetic energy of the charge particle is obtained by the potential energy of the field

So we will have

$KE = QV$

here we know that the charge on alpha particle is 2e and charge on proton is e

so we have

$\frac{1}{2}m_{\alpha}v_{\alpha}^2 = (2e)V$

$\frac{1}{2}m_{p}v_{p}^2 = (e)V$

now we can divide both equations

$\frac{m_{\alpha}v_{\alpha}^2}{m_pv_p^2} = 2$

also we know that

$m_{\alpha} = 4 m_p$

so we will have

$4\frac{v_{\alpha}^2}{v_p^2} = 2$

so we have

$\frac{v_{\alpha}}{v_p} = \sqrt{\frac{1}{2}}$

#Learn

Topic : Electrostatic energy of charge

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