An electron, an alpha-particle and a proton have the same kinetic energy. Which one of these particles has the largest de-Broglie wavelength?

As per the formula,

λ = \frac{h}{p}

Since,

λ = \frac{h}{mv}

Thus,

λ \propto \frac{1}{\sqrt{m}} .

Wavelength and mass has inverse dependence.

Since, mass of electron is the least out of all the three particles therefore, electron has the largest de-Broglie wavelength.

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