An electron, a proton, a deutron and an  α-particle have same linear momenta. Which one of them possesses least kinetic energy ?

Q: An electron, a proton, a deutron and an  α-particle have same linear momenta. Which one of them possesses least kinetic energy ?

(a) Electron

(b) Proton

(c) Deutron

(d)  α-particle

Ans: (d)

Sol: The relation between K.E & Linear Momentum is

$\displaystyle K = \frac{p^2}{2 m}$ ; p = Linear momentum

$\displaystyle K \propto \frac{1}{m}$ ; As p = constant

Since α-particle has larger mass , hence it has least kinetic energy .