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Task 2. Find the Thickness of Matter Calcium Required Attenuating Photon Radiation with an Energy of 0.3 MeV, and 3 Me V by a Factor of

Вопрос

Task 2. Find the thickness of matter Calcium required attenuating photon radiation with an energy of 0.3 MeV, and 3 Me V by a factor of 10.I Compare all results.

Решения

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ветеран · Репетитор 11 лет

Ответ

To find the thickness of matter required to attenuate photon radiation with a certain energy by a factor of 10, we can use the formula for attenuation: where:- is the intensity of the photon radiation after passing through a thickness of matter,- is the initial intensity of the photon radiation,- is the attenuation coefficient of the matter for the given photon energy,- is the thickness of the matter.We want to find the thickness such that . Rearranging the formula, we get: Dividing both sides by : Taking the natural logarithm of both sides: Now, we need to find the attenuation coefficient for calcium and the given photon energies.The attenuation coefficient is given by: where:- is the cross-section for attenuation,- is the number density of the matter (for simplicity, we assume 1 cm for this calculation).For calcium, the cross-section can be found using the atomic number and the energy of the photon. The cross-section can be approximated using the following formula: Now, let's calculate for the given photon energies:For MeV: For MeV: Now, we can calculate the thickness for each energy:For MeV: For MeV: Comparing the results, we can see that the thickness required for attenuation by a factor of 10 is inversely proportional to the attenuation coefficient . As the photon energy increases, the attenuation coefficient decreases, resulting in a larger thickness required for the same level of attenuation.