Give an expression for the minimum frequency of a photon that can form an electron and a positron by pair production - Leaving Cert Physics - Question (j) - 2013

To determine the minimum frequency of a photon required for pair production, we use the expression derived from Einstein's mass-energy equivalence and the principle of conservation of energy:

$f = \frac{2mc^2}{h}$

Here,

• $m$ is the mass of the electron (or positron), which is approximately $9.11 \times 10^{-31} \text{ kg}$,
• $c$ is the speed of light, approximately $3.00 \times 10^8 \text{ m/s}$,
• $h$ is Planck's constant, approximately $6.63 \times 10^{-34} \text{ Js}$.

This formula calculates the minimum frequency of the photon needed to create the electron and positron, considering that the energy of the photon must equal or exceed the total rest mass energy of the two particles combined.