Concept explainers
(a)
The amount of the energy released by the annihilation of an electron and a positron, if a positron has the same mass as an electron.
(a)
Answer to Problem 13Q
Solution:
Explanation of Solution
Given data:
The mass of the electron and the positron is the same.
Formula used:
According to the mass energy equation, the relation between energy and mass is:
Here, E is the energy released, m is the total mass of the positron and electron, and c is the speed of light,
Explanation:
The mass of the electron is
Then, the total mass of the electron and positron is,
Recall the expression for the mass-energy equation.
Substitute
Conclusion:
Therefore, the amount of energy released by the annihilation of electron and positron is
(b)
The wavelength of each photon. Also, confirm from figure 5-7 (from textbook) that this wavelength falls in the range of gamma-rays, if the products of the annihilation are two photons each of equal energy.
(b)
Answer to Problem 13Q
Solution:
Explanation of Solution
Given data:
The products of the annihilation are two photons, each of equal energy.
Formula used:
The expression for the relationship between energy and wavelength is:
Here,
Explanation:
Each photon receives half of the total energy released in annihilation. So, the energy received by each photon is
Recall the expression for the relationship between energy and wavelength.
Rearrange the above expression for
Substitute
Refer to figure 5-7 from the textbook and determine whether the calculated wavelength
Conclusion:
Therefore, this wavelength lies in the range of gamma-rays.
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