An electron and a positron annihilate each other, emitting two identical photons in the process. What is the wavelength of these photons? The mass of an electron or positron is 9.11 × 10^-31 kg and h = 6.63 × 10^-34 Js. A) 1.21 × 10^-12 m B) 1.73 × 10^-12 m C) 2.43 × 10^-12 m D) 3.07 × 10^-12 m E) 3.46 × 10^-12 m

Question

Quizplus · Accepted Answer

We can use conservation of energy and momentum to solve this problem. The rest mass energy of an electron or positron is given by E=mc^2, where m is the mass and c is the speed of light. The total rest mass energy of the electron and positron is therefore:

E = 2(mc^2) = 2(9.11 × 10^-31 kg)(299,792,458 m/s)^2 = 1.64 × 10^-13 J

This rest mass energy is converted completely into the energy of the two photons, since no other particles are produced. Each photon therefore has an energy of:

Eγ = E/2 = 8.21 × 10^-14 J

The energy of a photon is related to its wavelength by the equation Eγ = hc/λ, where h is Planck's constant. Solving for the wavelength gives:

λ = hc/Eγ = (6.63 × 10^-34 J s)(299,792,458 m/s)/(8.21 × 10^-14 J) = 2.43 × 10^-12 m

Therefore, the correct answer is choice C.

An Electron and a Positron Annihilate Each Other, Emitting Two