The wavelength of a subatomic particle is determined by its de Broglie wavelength, which can be expressed mathematically as:
λ= 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=mvTherefore, the wavelength can be rewritten as:
λ= Given that all particles have the same velocity "
v ", the wavelength is inversely proportional to the mass of the particle:
λ∝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
≈1.67×10−27kgNeutron (B): Mass
≈1.67×10−27kgAlpha particle (C): Mass
≈4.00×10−27kgElectron (D): Mass
≈9.11×10−31kgAmong 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]