Answer to Question #174538 in Atomic and Nuclear Physics for Charlotte

Question

A student is asked to use a computer simulation of radioactive decay. The sample chosen has a half-life of 2.5 hours and contains 38400 isotopes of radioactive material. Calculate the number of unstable nuclei remaining after 12.5 hours.

Answer 1

Let’s use the formula for radioactive decay:

$$N=N_0e^{-\dfrac{0.693}{T_{1/2}}t},$$ $$N=38400\cdot e^{-\dfrac{0.693}{2.5\ h}\cdot12.5\ h}=1201\ isotopes.$$