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A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of electron is $1.813×{10}^{-4}$. Calculate the particle's mass and indentify the particle.

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Explanation:

de Broglie wavelength of a moving particle, having mass m and velocity v:

$\lambda =h/p=h/mv\phantom{\rule{0ex}{0ex}}$

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For an electron, mass ${m}_{e}=h/{\lambda }_{e}{v}_{e}$

Now, we have                                        1/2mark

Then, mass of the particle,                                       1/2mark

m=$\left(9.11×{10}^{-31}kg\right)×\left(1/3\right)×\left(1/1.813×{10}^{-4}\right)$

m=$1×1.675×{10}^{-27}kg.$

Thus, the particle, with this mass could be a proton or a neutron.                       1/2mark

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