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Q12PE

Expert-verifiedFound in: Page 1238

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two **\({\rm{\gamma }}\)** rays of equal energy. What is the characteristic **\({\rm{\gamma }}\)**-ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such radiation is rarely observed is evidence that there is very little antimatter in the universe.) (b) How does this compare with the **\({\rm{0}}{\rm{.511 MeV}}\)** energy associated with electron-positron annihilation?**

- The characteristics of \(\gamma \) rays are found to be \(939\,{\rm{MeV}}\).
- The proton-antiproton annihilation energy is \(1.84 \times {10^3}\) times greater than electron-positron annihilation.

**In case of the annihilation if the mass gets converted into the energy. If we get value of total mass destroyed then the expression for the energy is obtained by,**

\(E = m{c^2}\)** **

**Here **\(E\)** is the energy, **\(m\)** is the mass and **\(c\)** is the speed of the light.**

We are using the conservation of energy and then evaluate:

\(E = {m_p}{c^2}\)

Here \({m_p}\) is the mass of the proton,

Substitute \(1.67 \times {10^{ - 27}}\,{\rm{kg}}\) for \({m_p}\) and \(3 \times {10^8}\,{\rm{m/s}}\) for \(c\) in the above equation.

\(\begin{array}{c}E = \left( {1.67 \times {{10}^{ - 27}}} \right){\left( {3 \times {{10}^8}} \right)^2}\\ = 15.0536 \times {10^{ - 11}}\,{\rm{J}}\end{array}\)

Convert into \({\rm{MeV}}\)

\(\begin{array}{c}E = \left( {15.05 \times {{10}^{ - 11}}\,{\rm{J}}} \right)\left( {6.242 \times {{10}^{12}}\,\frac{{{\rm{MeV}}}}{{\rm{J}}}} \right)\\ = 939\,{\rm{MeV}}\end{array}\)

Therefore the characteristics of \(\gamma \) rays are found to be \(939\,{\rm{MeV}}\).

Now compare the above calculated value with \(0.511\,\,{\rm{MeV}}\),

\(\begin{array}{c}Ratio = \frac{{939}}{{0.511}}\\ = 1.84 \times {10^3}\end{array}\)

Therefore the proton-antiproton annihilation energy is \(1.84 \times {10^3}\) times greater than electron-positron annihilation.

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