   Chapter 28, Problem 56PE

Chapter
Section
Textbook Problem

A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?

To determine

(a)

The energy released after the annihilation of a positron and an electron when the kinetic is negligible before the annihilation.

Explanation

Given:

Mass of electron, me=9.11×1031kg

Speed of light, c=3×108m/s

Formula used:

Formula to calculate the energy released after of a positron and an electron

E=Δmc2    ...... (I)

Calculation:

Since, a positron and an electron annihilate and both have equal mass. So, the total equivalent mass is the sum of the mass of the positron and the electron.

Calculate the energy released after the annihilation of the positron and the electron when the kinetic is negligible from equation (I).

E=Δmc2=(me+me)c2=2mec2

Substitute 9.11×1031kgfor meand 3×108m/sfor cto calculate the energy released in the above equation

To determine

(b)

The velocity of a proton when the energy release after the annihilation of the positron and the electron is given in the form of kinetic energy.

To determine

(c)

The velocity of an electron when the energy release after the annihilation of the positron and the electron is given in the form of kinetic energy.

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