Final answer:
To calculate the dose rate 2 m away from and along the center of the circular surface of the tank, we can use the concept of radioactivity and the inverse square law. The dose rate is one-fourth of the dose rate at a distance of 1 m.
Step-by-step explanation:
To calculate the dose rate 2 m away from and along the center of the circular surface of the tank, we can use the concept of radioactivity and the inverse square law. The radioactive material, 137Cs, is distributed uniformly within the tank. The dose rate is inversely proportional to the square of the distance from the source, so if the dose rate at a distance of 1 m is known, we can calculate the dose rate at a distance of 2 m.
First, we need to find the activity of 137Cs per unit volume in the tank. The volume of the tank can be calculated using the formula for the volume of a cylinder, V = πr²h, where r is the radius (half the diameter) and h is the height. Plugging in the values, we get V = π(0.25²)(2) = 0.3927 m³.
Next, we need to find the activity per unit volume. The total activity of 2 Ci is distributed within the tank, so the activity per unit volume is 2 Ci / 0.3927 m³ = 5.099 Ci/m³.
Now, we can calculate the dose rate at a distance of 1 m using the inverse square law. Let's assume that the dose rate at a distance of 1 m is D, and the distance at which we want to calculate the dose rate is 2 m. The dose rate at a distance of 2 m can be calculated using the formula D₂ = D₁ / (2²) = D / 4. Therefore, the dose rate 2 m away from and along the center of the circular surface of the tank is one-fourth of the dose rate at a distance of 1 m.