An electron and positron, each having kinetic energy 10 MeV, annihilate and produce two photons. What is the wavelength of each photon?
A) 0.124 pm
B) 0.118 pm
C) 0.248 pm
D) 0.062 pm
E) need more information

Question

Quizplus · Accepted Answer

The total energy of the electron and positron is given by E = 2(mc^2 + KE), where mc^2 is the rest energy of each particle and KE is the kinetic energy. Since the rest energy of an electron or positron is 0.511 MeV, we have E = 2(0.511 MeV + 10 MeV) = 21.022 MeV.

When the electron and positron annihilate, their total energy is converted into the energy of the two photons. Since each photon has energy E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength, we can solve for λ.

We have E = 2hc/λ, so λ = 2hc/E. Plugging in the values, we get:

λ = 2(6.626 x 10^-34 J s)(3 x 10^8 m/s)/(21.022 x 10^6 eV x 1.6 x 10^-19 J/eV)
   = 1.239 x 10^-6 m
   = 0.124 pm

Therefore, the wavelength of each photon is 0.124 pm, which corresponds to answer choice A.

An Electron and Positron, Each Having Kinetic Energy 10 MeV