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  4. If particles are moving with same velocity, then which has maximum de Broglie wavelength?

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Q. If particles are moving with same velocity, then which has maximum de Broglie wavelength?

AIPMTAIPMT 2002Dual Nature of Radiation and Matter

Solution:

de Broglie wavelength for a particle is given by $\lambda=\frac{h}{p}=\frac{h}{m v}$, where $m, v$ and $p$ are the mass, velocity and momentum respectively. $h$ is Planck's constant. Now, since all the particles are moving with same velocity, the particle with least mass will have maximum de-Broglie wavelength. Out of the given four particles (proton, $\alpha$-particles, i.e. He nucleus and $\beta$-particles, i.e. electrons) $\beta$-particles has the lowest mass and therefore it has maximum wavelength.