Question

An electron ,a proton and an alpha particle have the kinetic energy which one has the shortest wavelength

Answer 1

Since kinetic energy of the particles is the same, therefore, the heavier the particle, more its momentum and larger the momentum, shorter the deBroglie wave length. According, the shortest wavelength shall be of the alpha particle.

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Answer 2

$\huge \sf Alpha \: particles$

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★Since, de Broglie wavelength is given by

$\huge\tt \red{\lambda=\frac{h} {p} }$

Here, p is momentum of particle

Also know that

★Kinetic Energy :

$\huge\tt \orange{K=\frac{p^2} {2m}}$

If we solve,

$\large\tt{\lambda=\frac{h} {\sqrt{2mK} } }$

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

Therefore, the mass of proton $\large\tt{^1_1H}$

H is 1836 times more than an electron and mass of alpha particle $\large\tt{^4_2H}$

H four times that of proton.

Therefore alpha particles have higher wavelength.