Explain the radioactive decay of radium, with a half-life of 1590 years leads to the formation of an inert gas, radon, which decays with a half-life of 3.82 days. Both steps are first order processes. Presume that none of the radon escapes.
a) Making no approximations obtain an equation for the concentration of radon present as a function of time.
b) Find out the fraction of the original radium present after one year.