Question 3: An alpha particle has twice the charge of a beta particle. Why does the former deflects less than the later when passing between electrically charged plates, assuming they both have same speed.

ANSWER

An alpha particle is a helium nucleus having a mass of 4 amu and charge of +2e. On the other hand, a beta particle is relatively light and having charge –e.

Now the deflection of the particle is due to the acceleration the particle experiences while moving through the electric field.

Now for an α-particle,

Charge on the particle = 2e           Intensity of the electric field = E                 Mass of the particle = M

The force experienced by the particle in the field = 2Ee

This force will be equal to ma.

Therefore,           2eE = Ma ⇒ a = (2eE)/M … … … (1)

Similarly, for β particle, charge on the particle = e                         mass of the particle = m

Therefore,          a₁ = eE/m   … … …   (2)

Thus the acceleration (which determines the deflection) is directly proportional to the charge and inversely proportional to the mass of the particle.

Now charge of α particle is double the charge of the β particle. However, mass of the α particle is many times more than the mass of the β particle. The net effect is the acceleration produced in the β particle is more than the acceleration produced in α particle when passed through the same electrically charged plates. Therefore, a < a₁, and α particle will deflect less than the β particle in an electric field of intensity E if they are moving with the same speed.