Class 12 > Unit # 25: Quantum Physics > Pair Production & Annihilation of Matter

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Pair Production and Pair Annihilation

Video Lecture: Pair Production & Annihilation

Watch the complete video lecture explaining the conversion of photon energy into matter (pair production) and reverse annihilation:

Pair Production

Pair production is a crucial example demonstrating that photon energy can convert into kinetic energy as well as rest mass energy. A high-energy photon with energy $hf$ loses its entire energy when it interacts near a heavy atomic nucleus, creating a pair consisting of an electron and a positron while distributing any excess energy as kinetic energy to each particle.

Fig 1: High-energy photon converting into an electron-positron pair in the vicinity of a nucleus.

Momentum conservation in this process can be handled because the atomic nucleus is thousands of times more massive than the electron-positron pair, allowing it to absorb the required recoil momentum without absorbing a significant amount of energy. Thus, the process is primarily represented by an equation showing the conservation of total energy:

$hf = E_- + E_+$

$hf = (m_0 c^2 + K_-) + (m_0 c^2 + K_+)$

$hf = K_- + K_+ + 2m_0 c^2$     --- (i)

Where:

• $E_-$ and $E_+$ represent the total energies of the electron and positron respectively.
• $K_-$ and $K_+$ represent the kinetic energies of the electron and positron respectively.
• $m_0 c^2 = 0.511\text{ MeV}$ is the rest mass energy of an electron, which is equal to that of the positron.
• $2m_0 c^2 = 1.02\text{ MeV}$ represents the combined minimum threshold rest mass energy required to create the electron-positron pair.

Annihilation of Matter (Pair Annihilation)

Annihilation of matter is the exact reverse process of pair production. In pair annihilation, an electron and a positron in a stationary or low-energy state combine with each other and annihilate. The particles disappear entirely, and their mass-energy converts into radiation energy in the form of photons.

To conserve both energy and momentum, the most frequent process in pair annihilation is the creation of two photons traveling in exactly opposite directions with equal and opposite momenta (though sometimes three photons may be produced).

Fig 2: Annihilation of an electron-positron pair producing two oppositely directed gamma photons.

The energy balance equation for pair annihilation is represented as:

$K_- + K_+ + 2m_0 c^2 = 2 hf$     --- (ii)

Where:

• $K_-$ and $K_+$ represent the kinetic energies of the electron and positron before the collision.
• $2m_0 c^2$ represents the combined rest mass energy of both particles ($1.02\text{ MeV}$).
• $2hf$ represents the energy of the resulting photons after annihilation.

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