Question

An electron, an Alpha particle and a Proton have the same kinetic energy. Which of these particle has the shortest de Droglie wavelength?
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Answer 1

$\Large\bold{\underline{\underline{Answer:-}}}$

Alpha particle

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$\bf\small\bold{\underline{\underline{Step-By-Step\:Explanation:-}}}$

★Since, de Broglie wavelength is given by

$\bf\bold{\lambda=\frac{h} {p} }$

Here, p is momentum of particle

Also know that

★Kinetic Energy : $\bf\bold{K=\frac{p^2} {2m}}$

On solving $\bf\bold{\lambda=\frac{h} {\sqrt{2mK} } }$

Here, we can clearly see that de Broglie wavelength is inversely proportional to square root of their masses.

Therefore, the mass of proton $\bf{^1_1H}$ is 1836 times more than an electron and mass of alpha particle $\bf{^4_2H}$ four times that of proton.

Hence, alpha particle have shorter wavelength.

Answer 2

alpha has the shortest de-Broglie wavelength, because de -Broglie wavelength is inversely proportional to the mass of the particle.