Calculate the energy released by 1g of natural uranium assuming 200 MeV is released in each fission event and that the fissionable isotope ²³⁵U has an abundance of 0.7% by weight in natural uranium.

A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.

Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.

A uranium reactor develops thermal energy at a rate of 300 KW. Calculate the amount of ²³⁵U being consumed every second. Average energy released per fission is 200 MeV.

A town has a population of 1 million. The average electric power needed per person is 300W. A reactor is to be designed to supply power to this town. The efficiency with which thermal power is converted into electric power is aimed at 25%.

(a) Assuming 200 MeV of thermal energy to come from each fission event on an average, find the number of events that should take place every day.

(b) Assuming the fission to take place largely through ²³⁵U, at what rate will the amount of ²³⁵U decrease? Express your answer in kg per day.

(c) Assuming that uranium enriched to 3% in ²³⁵U will be used, how much uranium is needed per month (30 days)?