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

Question #282251

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


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



1
Expert's answer
2021-12-27T13:03:58-0500

A=mMNAln2T1/2,    A=\frac m M N_A\frac{\ln 2}{T^{1/2}},\implies

m=AMT1/2NAln2,m=\frac{AMT^{1/2}}{N_A \ln2},

m=13.710102261600365864006.0210230.69=1 g.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.


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