A Proton Races A Helium Nucleus

Electricity and Magnetism Level 2

An $\alpha$ -particle and a proton are accelerated at the same potential difference from rest.

If the ratio of their of their final velocities is in the form $\sqrt{a}$ where $a$ is a positive integer, submit your answer as $a$ .

The answer is 2.

1 solution

Rishabh Jain
Jan 30, 2016

K= $\frac{1}{2}mv^2 =qV$ (V-Potential Difference, v-velocity, m-mass,q-charge) $v∝\sqrt{\dfrac{q}{m}}$ $\dfrac{v_{\alpha}}{v_p}=\sqrt{\dfrac{q_{\alpha}m_p}{m_{\alpha} q_p}}$ $(Using~m_{\alpha}=4m_p~and~q_{\alpha}=2q_m)$ $=\sqrt{2}=\sqrt{a}$ $\Rightarrow \Large \color{#D61F06}{a=2}$

A Proton Races A Helium Nucleus

The answer is 2.

1 solution

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