Question

When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.

Required:
Write a differential equation that expresses the rate of change in the radiation level in terms of the radiation level.

Answer 1

The differential equation is
`(dR)/(dt) = -kR`

Explanation:

Differential equation for the rate of change in radiation level:

Radiation level is R.

Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:

`(dR)/(dt)`

After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.

Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:

`(dR)/(dt) = -kR`