In a process called pair production, a photon is transformed...

In a process called pair production, a photon is transformed into an electron and a positron. A positron has the same mass $\left(m_{e}\right)$ as the electron, but its charge is $+e$. To three significant figures, what is the minimum energy a photon can have if this process is to occur? What is the corresponding wavelength? The electron-positron pair will come into existence moving with some minimum amount of KE. The particles will separate, and as they do they will slow down. When far apart each will have a mass of $9.11 \times 10^{-31} \mathrm{~kg} .$ In effect, KE goes into $\mathrm{PE}$, which is manifested as mass. Thus, the minimum energy photon at the start of the process must have the energy equivalent of the free-particle mass of the pair at the end of the process. Hence,

In a process called pair production, a photon is transformed into an electron and a positron. A positron has the same mass $\left(m_{e}\right)$ as the electron, but its charge is $+e$. To three significant figures, what is the minimum energy a photon can have if this process is to occur? What is the corresponding wavelength?
The electron-positron pair will come into existence moving with some minimum amount of KE. The particles will separate, and as they do they will slow down. When far apart each will have a mass of $9.11 \times 10^{-31} \mathrm{~kg} .$ In effect, KE goes into $\mathrm{PE}$, which is manifested as mass.
Thus, the minimum energy photon at the start of the process must have the energy equivalent of the free-particle mass of the pair at the end of the process. Hence,

Key Concepts

Photon Energy–Wavelength Relationship

The photon energy–wavelength relationship, given by E = hc/?, links the energy of a photon to its wavelength, where h is Planck’s constant and c is the speed of light. This relationship allows one to convert between energy and wavelength, which is essential for determining the characteristic wavelength corresponding to the threshold energy in pair production.

Threshold Energy

Threshold energy refers to the minimum energy that a photon must have to initiate pair production. This energy is determined by the combined rest mass energy of the particle and its corresponding antiparticle, ensuring that enough energy is present to account for their masses according to mass–energy equivalence.

Pair Production

Pair production is a process in which a high-energy photon is converted into a particle–antiparticle pair. This phenomenon occurs when the energy of the photon is sufficient to produce the mass of both particles, and it demonstrates the interplay between energy and mass as described by modern physics.

Mass–Energy Equivalence

Mass–energy equivalence is a core principle of relativity encapsulated by the famous equation E = mc². It implies that mass can be converted to energy and vice versa, and in processes like pair production, the rest mass of the created particles determines the minimum energy required from the photon.

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