Answer to Question #282251 in Atomic and Nuclear Physics for BIGIRMANA Elie

Question

3. Show that the mass of radium (Mass number= 226, half-life = 1600 yrs) with an

activity of a curie (1Ci) is almost 1gm.

Answer 1

$A=\frac m M N_A\frac{\ln 2}{T^{1/2}},\implies$

$m=\frac{AMT^{1/2}}{N_A \ln2},$

$m=\frac{1\cdot 3.7\cdot 10^{10}\cdot226\cdot 1600\cdot 365\cdot 86400}{6.02\cdot 10^{23}\cdot0.69}=1~g.$