# A-level Physics (Advancing Physics)/Pair Production and Annihilation/Worked Solutions

h = 6.63 x 10−34 Js

1. The mass of an electron is 9.11 x 10–31 kg. What is the minimum amount of energy a photon must have to create an electron?

$E=2mc^{2}=2\times 9.11\times 10^{-31}\times (3\times 10^{8})^{2}=1.64\times 10^{-13}{\mbox{ J}}=1.02{\mbox{ MeV}}$ 2. A 1.1 MeV electron annihilates with a 1.1 MeV positron. What is the total energy of the photon produced?

2.2 MeV = 3.52 x 10−13 J

3. What is its frequency?

$f={\frac {E}{h}}={\frac {3.52\times 10^{-13}}{6.63\times 10^{-34}}}=5.31\times 10^{20}{\mbox{ Hz}}$ 4. What is its wavelength?

$\lambda ={\frac {c}{f}}={\frac {3\times 10^{8}}{5.31\times 10^{20}}}=5.65\times 10^{-13}{\mbox{ m}}$ 5. What classical physical conditions might cause a newly produced electron-positron pair to annihilate almost immediately?

Electrons and positrons have opposite charges, and so they attract each other. When they are created, they must have enough kinetic energy to escape each other's attraction. If this is not the case, they will annihilate.