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An electron and proton have the same de-...

An electron and proton have the same de-broglie wavelength. Which one of these has higher kinetic energy? Which one is moving faster?

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Let m and K be the mass and kinetic energy of a particle. Its de-Broglie wavelength is
`lambda=h/(sqrt(2mK)) or lambda^2=(h^2)/(2mK) or K=(h^2)/(2mlambda^2)`
i.e., `K prop1/m :' lambda` is for particles
`(K_e)/(K_p) =(m_p)/(M_e)gt1 or K_egtK_p`
Thus kinetic energy of electron is greater than that of proton. So the electron is moving faster.
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Knowledge Check

  • An electron and proton have the same de-Broglie wavelength. Then the kinetic energy of the electron is

    A
    Zero
    B
    Infinity
    C
    Equal to the kinetic energy of the proton
    D
    Greater than the kinetic energy of the proton

  • If a proton and electron have the same de Broglie wavelength, then

    A
    kinetic energy of electron `lt` kinetic energy of proton
    B
    kinetic energy of electron = kinetic energy of proton
    C
    momentum of electron = momentum of proton
    D
    momentum of electron `lt` momentum of proton

  • A photon and an electron moving with a velocity v have the same de broglie wavelength . Then the ratio of the kinetic energy of the electron to the kinetic energy of the photon is [C is the speed of light ]

    A
    a) `v/C`
    B
    b) `(2v)/(C )`
    C
    c) `(C )/(2v)`
    D
    d) `(v)/(2C)`

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