Task 3. The wavelength of primary photons is equal to 0.05 nm. 40000 photons passed through a region with an area 5cm^2 in a time 3 minutes. Find the Particle Fluence Rate after this radiation passes through thickness 8mm of beryllium.

To find the Particle Fluence Rate, we need to calculate the number of photons that interact with the beryllium layer and then determine the fluence rate based on the given area and time.<br /><br />First, let's calculate the number of photons that interact with the beryllium layer. We can use the formula for the interaction probability of photons with a material:<br /><br />\[ P = \mu \cdot x \]<br /><br />where \( P \) is the probability of interaction, \( \mu \) is the interaction coefficient, and \( x \) is the thickness of the material.<br /><br />Given that the wavelength of the primary photons is 0.05 nm, we can look up the interaction coefficient for beryllium at this wavelength. Let's assume the interaction coefficient is \( \mu = 10^7 \, m^{-1} \) (this value is for illustrative purposes and should be replaced with the actual value from experimental data or literature).<br /><br />Now, we can calculate the probability of interaction:<br /><br />\[ P = \mu \cdot x = 10^7 \cdot 8 \times 10^{-3} = 8 \times 10^4 \]<br /><br />Next, we need to find the fraction of photons that interact with the beryllium layer. This can be calculated as:<br /><br />\[ \text{Fraction of interacting photons} = 1 - e^{-P} = 1 - e^{-8 \times 10^4} \]<br /><br />Since \( P \) is very large, the exponential term will approach zero, and we can approximate:<br /><br />\[ \text{Fraction of interacting photons} \approx 1 \]<br /><br />Now, let's calculate the number of photons that interact with the beryllium layer:<br /><br />\[ \text{Number of interacting photons} = \text{Total number of photons} \times \text{Fraction of interacting photons} = 40000 \times 1 = 40000 \]<br /><br />Finally, we can calculate the Particle Fluence Rate. The fluence rate (\( \Phi \)) is defined as the number of particles per unit area per unit time. Given that the area is \( 5 \, cm^2 \) and the time is 3 minutes (180 seconds), we can calculate the fluence rate as:<br /><br />\[ \Phi = \frac{\text{Number of interacting photons}}{\text{Area} \times \text{Time}} = \frac{40000}{5 \times 10^{-4} \times 180} \]<br /><br />\[ \Phi = \frac{40000}{0.9} \approx 4.44 \times 10^4 \, \text{photons/} \, cm^2 \, s \]<br /><br />Therefore, the Particle Fluence Rate after the radiation passes through the thickness of 8 mm of beryllium is approximately \( 4.44 \times 10^4 \, \text{photons/} \, cm^2 \, s \).