COMEDK 2024 Shift 1 Paper

The wavelength of a subatomic particle is determined by its de Broglie wavelength, which can be expressed mathematically as:
λ=‌

h

p

where:
λ = wavelength
h= Planck's constant
p= momentum
Momentum ( p ) is given by the product of the mass (m) and velocity (v) of the particle:
p=mv
Therefore, the wavelength can be rewritten as:
λ=‌

h

mv

Given that all particles have the same velocity " v ", the wavelength is inversely proportional to the mass of the particle:
λ∝‌

1

m

This means that the particle with the largest mass will have the shortest wavelength. Let's compare the masses of the given subatomic particles:
Proton (A): Mass ≈1.67×10−27‌kg
Neutron (B): Mass ≈1.67×10−27‌kg
Alpha particle (C): Mass ≈4.00×10−27‌kg
Electron (D): Mass ≈9.11×10−31‌kg
Among these, the alpha particle has the highest mass. Therefore, the alpha particle will have the shortest wavelength.
So, the correct answer is:
Option C: [C]