Radioactive activity — UPSC Physics Optional CSE 1990 Paper II

Radium has a half-life of 1600 years and the daughter nucleus Radon also decays with a half-life of 3.82 days. In an enclosure containing radium and radon gas, the amount of radon appears to be constant for observations extending over a week. Explain this and calculate the ratio of the numbers of radium nuclei. Will the amount of radon remain the same even after 400 years?