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Ratio of de Broglie wavelengths from masses and speeds

This type of question, asked 4 times: 2021 Paper 4, 2021 Paper 9, 2021 Paper 14, 26 Jul 2022. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 4

    11
    An electron of mass mem_{e} and a proton of mass mp=1836mem_{p}= 1836m_{e} are moving with the same speed. The ratio of their de Broglie wavelength λelectron λproton \frac{\lambda_{\text{electron~}}}{\lambda_{\text{proton~}}} will be:

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  2. Question 2

    2021 Paper 9

    13
    A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2:12:1, the mass of the particle is:-

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  3. Question 3

    2021 Paper 14

    16
    A nucleus of mass 4 m4\text{ }m disintegrates into two daughter nuclei of mass mm and 3 m3\text{ }m. Find the ratio of their respective De Broglie wavelength?

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  4. Question 4

    26 Jul 2022

    100
    A nucleus of mass MM at rest splits into two parts having masses M′3\frac{M^{'}}{3} and 2M′3(M′<M)\frac{2M^{'}}{3}\left( M^{'}< M \right). The ratio of de Broglie wavelength of two parts will be:

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