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    Question

    An electron and a proton are accelerated by the same

    potential difference. Which one has a longer de Broglie wavelength?
    A Proton Correct Answer Incorrect Answer
    B Electron Correct Answer Incorrect Answer
    C Both same Correct Answer Incorrect Answer
    D Depends on charge sign Correct Answer Incorrect Answer

    Solution

    When an electron and a proton are accelerated through the same potential difference, they both gain the same kinetic energy (since K.E. = qV, and both have equal magnitude of charge). The de Broglie wavelength is given by: λ = h / √(2mK.E.) For equal kinetic energy:

    • λ ∝ 1 / √m
    Since the electron has a much smaller mass than the proton, it will have a longer de Broglie wavelength.

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