Design the smallest cubical uniform nuclear reactor which will have a fission rate at any point not greater than 2.1*1011 fissions.cm-3.s-1 and a fission power not smaller than 2,500 MW. [Neglect the extrapolation distance.]
To design the smallest cubical uniform nuclear reactor meeting the given specifications, we need to calculate the necessary dimensions based on the fission rate and fission power requirements. Here's how we can approach this problem:
Step 1: Calculate the required total fissions per second:
Fission rate = 2.1 * 10^11 fissions.cm^(-3).s^(-1)
Volume of the reactor = (side length)^3
Total fissions per second = Fission rate * Volume of the reactor
Step 2: Calculate the total fission power:
Fission power = 2,500 MW
Total fission power = Fission power * Total fissions per second
Step 3: Determine the dimensions of the cubical reactor:
Let's assume the side length of the reactor as 'L' cm.
Volume of the reactor = L^3
Step 4: Equate the total fission power equation and solve for the side length 'L':
Total fission power = Fission power * Total fissions per second
2,500 MW = (2.1 * 10^11 fissions.cm^(-3).s^(-1)) * (L^3) * (1.602 * 10^(-10) J per fission) * (1 MW / 10^6 J.s^(-1))
Simplifying the equation, we find:
L^3 = (2,500 * 10^6 * 10^5) / (2.1 * 1.602)
L^3 = (2,500 * 10^18) / (2.1 * 1.602)
L^3 ≈ 7.292 * 10^17
Taking the cube root on both sides, we get:
L ≈ 904 cm
Therefore, the side length of the smallest cubical uniform nuclear reactor that meets the given specifications is approximately 904 cm.