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When a proton encounters an antiproton, the two particles annihilate each other, producing two gamma rays. Assuming the particles were at rest when they annihilated, find the energy of each of the two gamma rays produced. (Note: The rest energies of an antiproton and a proton are identical.)

Short Answer

Expert verified
Each gamma ray has an energy of approximately \(1.50 \times 10^{-10}\) J.

Step by step solution

01

Identify the Rest Energy of Proton and Antiproton

Both the proton and antiproton have a rest energy equivalent to their mass. The rest energy can be found using the equation \(E = mc^2\), where \(m\) is the mass of the proton (approximately \(1.67 \times 10^{-27}\) kg), and \(c\) is the speed of light (\(3.00 \times 10^8\) m/s).
02

Calculate the Rest Energy of a Single Proton or Antiproton

Using \(E = mc^2\), the rest energy of a proton or antiproton is calculated as follows:\[ E = (1.67 \times 10^{-27} \text{ kg})(3.00 \times 10^8 \text{ m/s})^2 \approx 1.50 \times 10^{-10} \text{ J} \]
03

Total Energy Released from Annihilation

Since both the proton and antiproton annihilate, the total rest energy is the sum of their individual energies:\[ E_{\text{total}} = 2 \times 1.50 \times 10^{-10} \text{ J} \approx 3.00 \times 10^{-10} \text{ J} \]
04

Equate Total Energy to Energy of Gamma Rays

The energy from the annihilation process gets converted into two gamma rays, meaning each gamma ray carries half of the total energy:\[ E_{\gamma} = \frac{E_{\text{total}}}{2} = \frac{3.00 \times 10^{-10} \text{ J}}{2} \approx 1.50 \times 10^{-10} \text{ J} \]
05

Conclusion on the Energy of Each Gamma Ray

Each of the two gamma rays produced in the annihilation will have an energy of approximately \(1.50 \times 10^{-10} \text{ J}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

gamma rays
Gamma rays are a form of electromagnetic radiation that possesses the shortest wavelength and highest energy within the electromagnetic spectrum. This makes them exceptionally powerful and energetic compared to other forms of light, like visible light or X-rays. During a particle annihilation event, such as a proton-antiproton collision, gamma rays are frequently produced.
When these subatomic particles annihilate, their mass is converted into energy according to the principle of mass-energy equivalence described by Einstein's equation, \(E=mc^2\). In the context of our exercise, the energy from the annihilation is emitted as gamma rays. This is why they are often observed in high-energy events and considered fundamental for understanding atomic and subatomic processes.
  • Gamma rays are capable of penetrating most materials, which makes them both useful in medical imaging and industrial applications, but also requires cautious handling due to their potential to cause harm to living tissues.
  • In particle physics, detecting gamma rays helps scientists to study events that release large amounts of energy, like supernovae or the collision of particles in accelerators.
rest energy
Rest energy is a term in physics that encapsulates the energy equivalent of an object's mass when it is at rest. The concept stems from Einstein's well-known equation, \(E=mc^2\), where \(E\) represents energy, \(m\) is mass, and \(c\) is the speed of light (approximately \(3.00 \times 10^8\) m/s).
This equation conveys that a resting mass possesses intrinsic energy, regardless of its state of motion. For subatomic particles like protons or antiprotons, rest energy plays a crucial role since these particles are foundational components of matter.
  • In the scenario of proton-antiproton annihilation, each particle converts its rest energy into the energy of gamma rays. This transformation underlines the concept that mass and energy are interchangeable.
  • The rest energy of a proton—or an antiproton—is significant because it sets a baseline energy transformation potential when these particles engage in reactions.
Understanding rest energy allows physicists to predict energy output during annihilation events, helping them to piece together the dynamics of particle interactions at a fundamental level.
proton-antiproton annihilation
Proton-antiproton annihilation is a fascinating process in particle physics where a proton and its antimatter counterpart, the antiproton, meet and eliminate each other. This annihilation results in the release of significant energy in the form of gamma rays, as described by the mass-energy equivalence principle (\(E=mc^2\)).
The intriguing aspect of this interaction lies in its efficiency; the mass of both particles is completely transformed into energy. Unlike chemical reactions, which only release a fraction of the energy in viable bonds, annihilation events utilize the full rest mass of the particles.
  • Because protons and antiprotons have identical masses but opposite charges, their annihilation is highly symmetric, resulting in two gamma rays with equal energy being produced.
  • This phenomenon not only illustrates the conversion of matter into pure energy but also aids in studying the properties of antimatter and its interactions with normal matter.
The study of proton-antiproton annihilation not only enhances our understanding of fundamental physical laws but also reinforces the practical application of theoretical physics concepts like symmetry, conservation of energy, and the dynamics of particle interactions.

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