Find the ratio of speeds of a proton and an alpha particle accelerated through the same voltage, assuming nonrelativistic final speeds. Take

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.

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Nho 5 years 2021-07-18T22:01:10+00:00 1 Answers 25 views 0

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  1. danthu
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    2021-07-18T22:03:06+00:00
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    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.

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