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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Инесса
Экспертная проверка
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.