A hypothetical particle has a mass 512eV/c^2.If such a particle at rest decays into two gamma-rays photons, what is the wavelength of each photon?
1 Answer
Mass of hypothetical particle
Using Einstein's Mass-Energy relation, its energy
Particle decays in two
Momentum of a photon is equal to Planck's constant divided by the wavelength of the photon
#p=h/lambda#
Using law of Conservation of momentum, we see that momentum of one gamma ray photon must be equal and opposite to the momentum of other photon.
#=># Wavelength of both photons must be equal.
As such each photon must have energy
Now from Planck's-Einstein equation
#=>lambda=(hc)/E_gamma#
where Planck's constant#h=4.136 xx 10^-15 eV s# and velocity of light#c=3xx10^8\ ms^-1#
Inserting given values we get
#lambda=(4.136 xx 10^-15 xx3xx10^8)/256#
#lambda=4.846875\ nm#