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University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
BuyFindarrow_forward

University Physics Volume 3

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

When an electron and positron collide at the SLAC facility, they each have 50.0-GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

To determine

The collision energy when an electron and positron collide, both having an initial kinetic energy of 50 GeV.

Explanation

Given:

Initial Kinetic energy of electron = Initial kinetic energy of positron = Ei = 50GeV.

Formula used:

When an electron collides with a positron and annihilation occurs, then both the electron and the positron will each release total energy E=Ei+Er, where,

  Er is the relativistic kinetic energy, given by Er = mc2, m being the mass of electron/positron and c, the speed of light.

Calculation:

As per the formula, taking into account the annihilation of the two masses,

The energy released by electron, E1=Ei+Er

Since the positron also has the same mass and kinetic energy as the electron, so the positron will also release the same amount of energy, given by, E2=Ei+Er.

The total available energy is given by

  E=E1+E2=2(Ei+Er)

We know that mass of the electron m=9.11×1031 kg, and speed of light c=3×108 m/s

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