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De Broglie wavelengths of different charged particles accelerated through a potential

This type of question, asked 3 times: 17 Apr 2026 S2, 20 Apr 2026 S1, 20 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    17 Apr 2026 S2

    144
    The ratio of the accelerating potentials required to accelerate (i) an α\alpha-particle and (ii) a proton to have the same de Broglie wavelength associated with them is (mass of α\alpha - particle = 6.4×10−276.4 \times 10^{-27} kg, mass of proton = 1.6×10−271.6 \times 10^{-27} kg)

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  2. Question 2

    20 Apr 2026 S1

    144
    The proton and α\alpha - particle are accelerated through same potential difference. Then the ratio of the de-Broglie wavelength of proton and α\alpha - particle is (mass of α\alpha-particle is 44 times mass of proton, charge of α\alpha-particle is 22 times charge of proton)

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  3. Question 3

    20 Apr 2026 S2

    145
    The ratio of de-Broglie wavelength of an α\alpha-particle and proton accelerated from rest by the same potential is 1m\dfrac{1}{\sqrt{m}}. The value of mm is

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