Compare the amount of energy released when a proton and antiproton annihilate each other to the

Compare the amount of energy released when a proton and...

Key Concepts

Nuclear Fusion

Nuclear fusion involves the combining of lighter atomic nuclei, such as protons, to form a heavier nucleus, like helium. This process, which powers stars, releases energy as a result of the slight difference in mass between the reactants and the product, with the lost mass converted into energy. However, the energy per reaction is generally lower than that of full mass-energy conversion seen in particle-antiparticle annihilation.

Particle-Antiparticle Annihilation

This concept refers to the process where a particle and its corresponding antiparticle, such as a proton and an antiproton, collide and annihilate each other, converting their entire rest mass into energy. The mass-energy equivalence principle is central here, as it indicates that the energy released during such an event is extremely high, given that all of the mass is transformed into energy, typically in the form of high-energy photons.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated by Einstein’s equation E=mc^2, is the principle that mass can be converted into energy and vice versa. This fundamental concept underlies both nuclear fusion and particle-antiparticle annihilation, allowing for quantitative comparisons of energy release by relating the amount of mass lost in a reaction to the energy produced.

Transcript

00:02 So this question involves the calculation of the energies of two gamma rays that are produced in a proton -antiproton annihilation.

00:13 Now we're going to invoke two principles here, they're both conservation principles.

00:17 One of them is the conservation of energy.

00:22 That is to say, the energy initially here is the rest energy of the proton and the antiproton.

00:30 If we have a proton and an antiproton and they're not moving, they're at rest initially, then the only energies present initially are the rest energies of the proton and antiproton.

00:43 The rest energy given to us by the formula, the rest energy is equal to the rest mass times the speed of light squared.

00:56 Each of them has that much rest energy.

00:59 Now when they annihilate, they produce two gamma rays.

01:03 And by conservation of energy, the energy, total energy of those two gamma rays must equal the energy that was present initially.

01:15 So the total energy must be the sum of those two rest energies of the proton and the antiproton.

01:23 But let's talk about the two gamma rays, what we get from conservation momentum.

01:28 We have two gamma rays and they're flying off and they must be flying off in opposite directions.

01:36 And they must have the same magnitude of momentum.

01:38 Here's why.

01:40 We have a gamma ray here and a gamma ray here.

01:43 The total momentum using the conservation of momentum must be zero after the annihilation is the same as it was before.

01:52 Because momentum is still conserved.

01:54 And the only way for the total momentum to be zero afterwards is if the two gamma rays are flying off in opposite directions and have an equal magnitude of momentum.

02:08 Gamma rays, they are photons, they do have momentum...

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