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Two gamma photons are produced when a muon and an antimuon annihilate each other - AQA - A-Level Physics - Question 10 - 2018 - Paper 1

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Two gamma photons are produced when a muon and an antimuon annihilate each other. What is the minimum frequency of the gamma radiation that could be produced?

Worked Solution & Example Answer:Two gamma photons are produced when a muon and an antimuon annihilate each other - AQA - A-Level Physics - Question 10 - 2018 - Paper 1

Step 1

Identify the Energy Released

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Answer

The annihilation of a muon and an antimuon produces two gamma photons. According to the principles of energy conservation in particle physics, the energy of the annihilated particles is converted into the energy of the photons. We can use the mass-energy equivalence formula:

E=mc2E = mc^2

where mm is the mass of the muon and antimuon, and cc is the speed of light.

Step 2

Calculate the Frequency of the Gamma Radiation

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The energy of a photon can also be expressed as:

E=hfE = hf

where hh is Planck's constant and ff is the frequency of the photon. To find the minimum frequency, we can equate the energy of the photons produced with the energy released during annihilation:

hf=2mc2hf = 2mc^2

Thus, the frequency is given by:

f=2mc2hf = \frac{2mc^2}{h}

By substituting the mass of the muon (which is approximately 1.88×10−281.88 \times 10^{-28} kg) and known constants, we can calculate the minimum frequency.

Step 3

Select the Correct Answer

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After performing the calculations, we find that the minimum frequency of the gamma radiation that could be produced is 5.10×1016Hz5.10 \times 10^{16} Hz. Therefore, the correct answer is:

Answer B: 5.10 x 10^16 Hz

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