An electron with kinetic energy 589 keV collides with a positron of the same kinetic energy moving in the opposite direction.Calculate the wavelength of the two identical photons produced in the annihilation. A)4.22 $\times$ 10^-3 nm B)1.13 $\times$ 10^-3 nm C)2.11 $\times$ 10^-3 nm D)2.26 $\times$ 10^-3 nm E)2.26 $\times$ 10^-3 m

Question

Quizplus · Accepted Answer

In annihilation, the total energy of the electron and positron is converted to the energy of two identical photons.
Given kinetic energy of each electron and positron = 589 keV
Total energy of electron and positron = 2 * 589 keV
Energy of two identical photons after annihilation = 2 * 589 keV = 1178 keV
Using E=hc/λ, we can find the wavelength of the photons:
λ = hc/E
= (6.626 * 10^-34 J s * 3 * 10^8 m/s) / (1178 keV * 1.602 * 10^-19 J/keV)
= 1.13 * 10^-3 nm = 1.13 Å
Therefore, the correct choice is B.

An Electron with Kinetic Energy 589 KeV Collides with a Positron