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Particles with given de Broglie wavelengths: compare their velocity, momentum or kinetic energy

This type of question, asked 6 times: 2021 Paper 2, 2021 Paper 22, 1 Feb 2023, 8 Apr 2023, 1 Feb 2024, 8 Apr 2024. All 7 questions below, oldest first.

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  1. Question 1

    2021 Paper 2

    16
    The de Broglie wavelength of a proton and α\alpha-particle are equal. The ratio of their velocities is:

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  2. Question 2

    2021 Paper 22

    19
    A moving proton and electron have the same deBroglie wavelength. If KK and PP denote the K.E. and momentum respectively. Then choose the correct option:

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  3. Question 3

    1 Feb 2023

    12
    A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ\lambda. An alpha particle having certain kinetic energy has the same de Broglie wavelength λ\lambda. The ratio of kinetic energy of proton and that of alpha particle is:

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  4. Question 4

    8 Apr 2023

    20
    Proton (P) and electron (e) will have same deBroglie wavelength when the ratio of their momentum is (assume, mp=1849 mem_{p}= 1849{\text{ }m}_{e} )

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  5. Question 5

    1 Feb 2024

    11
    The de Broglie wavelengths of a proton and an α\alpha particle are λ\lambda and 2λ2\lambda respectively. The ratio of the velocities of proton and α\alpha particle will be:

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  6. Question 6

    8 Apr 2024

    3
    A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h=6.63×10−34 J s, me=9.0×10−31 kgh = 6.63 \times10^{- 34}\text{ }J\text{ }s,{\text{ }m}_{e}= 9.0 \times10^{- 31}\text{ }kg and mp=1836m_{p}= 1836 times mem_{e} )

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  7. Question 7

    8 Apr 2024

    107
    A proton and an electron have the same de Broglie wavelength. If KpK_{p} and KeK_{e} be the kinetic energies of proton and electron respectively. Then choose the correct relation:

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