Question

Electron,proton, neutron and alpha particle have same momentum which particle has more kinetic energy?

Answer 1

Smaller the mass of the particle, larger its kinetic energy.

Explanation:

Let `M` be the constant momentum, then as `M=mv`, where `m` is mass and `v` is velocity, then `vprop1/m`

and as kinetic energy (`KE`) is given by `1/2mv^2`, we have

`KEpropmv^2` or `KEprop(mxx1/m^2)`

i.e. `KEprop1/m`

Hence smaller the mass of the particle, larger its kinetic energy

i.e. electron has most kinetic energy.

Answer 2

Kinetic energy in terms of momentum `vecp` is given by the expression

`KE=|vecp|^2/(2m)`
where `m` is the mass of particle.

It is given that momentum of all four particles Electron, proton, neutron and alpha particle is same. Above expression reduces to

`KEprop1/m`

Out of given particles, electron has the lowest mass. Therefore, electron has the maximum kinetic energy.