Cesium 137 (Cs¹³⁷)is a Short-Lived Radioactive Isotope $e^{-\left(\frac{\ln 2}{30}\right) t}$

question 127

Short Answer

Cesium 137 (Cs¹³⁷)is a short-lived radioactive isotope.It decays at a rate proportional to the amount of itself present and has a half-life of 30 years (i.e., the amount of Cs¹³⁷ remaining t years after A₀ mg of the radioactive isotope is released is given by $e^{-\left(\frac{\ln 2}{30}\right) t}$ ).As a result of its operations, a nuclear power plant releases Cs¹³⁷ at a rate of 0.14 mg per year.The plant began its operations in 1990, which we will designate as t = 0.Assume there is no other source of this particular isotope.Since Cs¹³⁷ poses a great health risk, the government says that the maximum amount of Cs¹³⁷ acceptable in the surrounding environment is 1 mg (spread over the surroundings).How many mg per year of the isotope can the station release and still be in compliance with the regulations? Round to 2 decimal places.

---

Definitions:

Carotid Baroreceptors

Sensory nerve endings located in the carotid artery that detect changes in blood pressure and help regulate it.

Glossopharyngeal Nerve

The ninth cranial nerve, responsible for sensory and motor functions in the throat and back of the tongue.

Sympathetic Nerve

The sympathetic nervous system is part of the autonomic nervous system that prepares the body for 'fight or flight' responses during perceived threats.

Carotid Baroreceptors

Sensors located in the carotid arteries that monitor blood pressure and relay information to the central nervous system to maintain stable blood pressure.