An electron and a proton have their masses in the ratio 1:1840. What will be the ratio of their kinetic energy if they have equal momentum?<

Question

An electron and a proton have their masses in the ratio 1:1840. What will be the ratio of their kinetic energy if they have equal momentum?

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Thu Thảo 4 years 2021-08-03T20:14:52+00:00 1 Answers 218 views 0

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  1. Tryphena
    0
    2021-08-03T20:16:02+00:00
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    Answer:

    1840:1

    Explanation:

    If m is the mass of the electron, and 1840m is the mass of the proton, then:

    p₁ = p₂

    m₁v₁ = m₂v₂

    m v₁ = 1840m v₂

    v₁ = 1840 v₂

    The kinetic energy of the electron is:

    KE₁ = ½ m₁ v₁²

    KE₁ = ½ m (1840 v)²

    KE₁ = 1692800 mv²

    The kinetic energy of the proton is:

    KE₂ = ½ m₂ v₂²

    KE₂ = ½ (1840m) v₂²

    KE₂ = 920 mv²

    The ratio of the kinetic energies is:

    KE₁ / KE₂

    (1692800 mv²) / (920 mv²)

    1840:1

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