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  4. If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?

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Q. If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?

J & K CETJ & K CET 2011Dual Nature of Radiation and Matter

Solution:

As per the formula,
$\lambda=\frac{ h }{ p }$
Since $\lambda=\frac{ h }{ mv }$
thus, $\lambda \propto \frac{1}{\sqrt{ m }}$
Wavelength and mass has inverse dependence.
Since, mass of electron is the least out of all the three particles . ., electron has the largest de-Broglie wavelength.