When subatomic particles undergo reaction energy is conserved, but mass is not necessarily conserved. However, a particle's mass 'contributes' to its total energy, in accordance with Einstein'f famouns equation, `E= mc^(2)`
In this question, `E` denotes the equivalent energy when a particle of mass `m` is converted into energy. The particle can also have additional energy due to its motion and its interactions with other particles.
Consider a neutron at rest, and well separated from other particles. It decays into a proton, an electron, and an undetected third particle: `"Neutron"rarr"proton"+"electron"+"third particle"`
The table below summarizes some data from a single nuetron decay. Column `2` shows the rest mass of the particle times the speed of light squared.
`{:("Particle",Mx C^(2),,"Kinetic Energy",),(,(MeV),,(MeV),),("Neutron",940.97,,0,),("Proton",939.66,,0.02,),("Electron",0.51,,0.42,):}`
Consider an ensemble of particles, all of which have the same positive kinetic energy but different masses. For this ensemble, which graph best represents the relationship between the particle's mass and its total energy ?

Options

A.
B.
C.
D.

Answer

C

Explanation

But E varies linearly with m. Since the particle in the ensemble all have positive kinetic energy, the total energy is positive even when the mass is zero [relativistic physics permits this, because kinetic energy no longer equals `(1//2)mv^(2)`. So, the graph does not begin at the origin.