Radioactive radon-222 gas (222rn) occurs naturally as a product of uranium decay. the half-life of 222rn is 3.8 days. suppose a flask originally contained 4.0×1013 atoms of 222rn. how many atoms of 222rn will remain after one month (30. days)?

Radioactivity is the process by which unstable isotope losses energy by emitting radiations such as alpha radiation, gamma radiation or beta radiations to attain stability. Half life is the time taken by a radioisotope or a radioactive substance to decay by half its original amount.
New mass = original mass × (1/2)n where n is the number of half lives
 In this case, the half life is 3 days, thus in 30 days the number of half lives will be 7.895. 
Hence, New atoms = 4.0 × 10^13 × (1/2)^7.895
                                = 1.6805 × 10^11 atoms

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