Question

Find the ratio of speeds of a proton and an alpha particle accelerated through the same voltage, assuming nonrelativistic final speeds. Take the mass of the alpha particle to be 6.64 ✕ 10−27 kg.

Answer 1

Answer:

The required ratio is 1.99.

Explanation:

We need to find the atio of speeds of a proton and an alpha particle accelerated through the same voltage.

We know that,

$eV=\dfrac{1}{2}mv^2$

The LHS for both proton and an alpha particle is the same.

So,

$\dfrac{v_p}{v_a}=\sqrt{\dfrac{m_a}{m_p}} \\\\\dfrac{v_p}{v_a}=\sqrt{\dfrac{6.64\times 10^{-27}}{1.67\times 10^{-27}}} \\\\=1.99$

So, the ratio of the speeds of a proton and an alpha particle is equal to 1.99.