An electron and a positron,both essentially at rest,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.(h = 6.626 × 10^-34 J ∙ s,c = 3.00 × 10⁸ m/s) A)1.21 × 10^-12 pm B)1.73 pm C)2.42 pm D)3.07 pm E)3.46 pm

Question

Quizplus · Accepted Answer

When the electron and positron annihilate, their combined rest mass energy is converted into the energy of two photons. Since the two photons are identical, they must share this energy equally. Therefore, the energy of each photon is:

E = (total energy)/(number of photons) = (mec^2 + mpc^2)/2 = (2 x 9.11 x 10^-31 kg x (3 x 10^8 m/s)^2)/2 = 1.64 x 10^-13 J

The wavelength of a photon is given by:

λ = hc/E

where h is Planck's constant and c is the speed of light. Substituting in the values, we get:

λ = (6.626 x 10^-34 J.s x 3 x 10^8 m/s)/(1.64 x 10^-13 J) = 1.21 x 10^-12 m = 1.21 pm

Therefore, the correct choice is C, 2.42 pm, since the question asks for the wavelength in picometers.

An Electron and a Positron,both Essentially at Rest,annihilate Each Other,emitting