3. Show that the mass of radium (Mass number= 226, half-life = 1600 yrs) with an
activity of a curie (1Ci) is almost 1gm.
A=mMNAln2T1/2, ⟹ A=\frac m M N_A\frac{\ln 2}{T^{1/2}},\impliesA=MmNAT1/2ln2,⟹
m=AMT1/2NAln2,m=\frac{AMT^{1/2}}{N_A \ln2},m=NAln2AMT1/2,
m=1⋅3.7⋅1010⋅226⋅1600⋅365⋅864006.02⋅1023⋅0.69=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.m=6.02⋅1023⋅0.691⋅3.7⋅1010⋅226⋅1600⋅365⋅86400=1 g.
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