University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185

University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

When both an electron and a positron are at rest, they can annihilate each other according to the reaction e + e + γ + γ . In this case, what are the energy, momentum, and frequency of each photon?

To determine

The energy, momentum and frequency of each photon.




Formula used:

The momentum of a photon is calculated by


Frequency of photon is calculated by



As an electron and a positron is anti-matter of one another the energy of an electron is equal to the energy of a positron which is 0.511 MeV

The given relation is


The reactant consists of an electron and a positron. So the total energy will be twice the energy of 0.511MeV. According to the law of conservation of energy the energy of the reactant should be equal to the energy of the product. So the energy of the products will be 1.022 MeV and hence the energy of each photon will be 0.511MeV.

As 1.0MeV is equal to the energy value of 0.511 MeV in terms of Joules is

  0.511MeV=0.511MeV(1.602× 10 13J1.0MeV)


The relation between energy and frequency is


Where E is the energy, h is the Plank's constant and v is the frequency. Using the values of energy obtained and the frequency is calculated as follows.


  v=Ehv=8.19× 10 14J6.626× 10 34Jsv=1.2×1020s1=1

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