Radium 2~:Ra has a half-life of about 3.6 days (a) Given 1 gram, how much will stìll be present after 1 day? (b) After 1 year?

(a) The mass of radium (m) left after a period of time (t) is given by,
m = (mo)/2^n
where (mo) is the initial mass, and n is the no. of half-lives lapsed, which is equal to t/T (T is the half-life)

Now, after 1 day, n = 1/3.6 = 0.2778
Hence, mass of radium left = 1/(2^0.2778) gram = 0.825 gram

(b) 1 year = 365 days
thus after 1 year, n = 365/3.6 = 101.4
Amount left after 1 year = 1/(2^101.4) gram = 3 x 10^-31 gram