Question 19: If the following particles all have the same K.E, which has the shortest wavelength? Electron, alpha particle, neutron and photon.
We know the Kinetic energy in terms of momentum of a moving particle is (E = p2/2m). Here p is the linear momentum and m is the mass of the particle. Therefore,
Similarly, the de’ Broglie wave associated with a moving particle is λ = h/p. Put the value of p from (1)
In the given condition, E is same for all particles. Also h is a constant. The first part on the RHS of this equation is constant and therefore, wavelength is inversely proportional to the square root of the mass of the particle. .
This proportionality means the de’ Broglie wave associated with a particle is inversely proportional to the square root of the mass of the particle. Larger the mass, smaller the wavelength.
Now in the given set of particles, alpha particle is the heaviest. Therefore, alpha particle would have the shortest wavelength under the condition of same kinetic energy.