Discussion
Out of the following particles, all having the same kinetic energy, which has the longest wavelength ?
Answer: B
The longest wavelength belongs to an electron.
The de Broglie wavelength of a particle with kinetic energy K is
\[ \lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}} \]
At the same kinetic energy, \(\lambda \propto 1/\sqrt{m}\), so the lightest particle has the longest wavelength. The electron is about 1836 times lighter than a proton, so its wavelength is about 43 times longer. The proton and neutron have nearly equal masses and wavelengths, and the alpha particle, about four times heavier still, has the shortest.
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