The age of a continental crust sample can be estimated from minerals containing samarium (Sm) and neodymium (Nd). 62147Sm^{147}_{62}\text{Sm}62147Sm decays to 60143Nd^{143}_{60}\text{Nd}60143Nd with a radioactive decay constant of 6.54×10−12 year−16.54 \times 10^{-12} \text{ year}^{-1}6.54×10−12 year−1.
Calculate, in years, the half-life of 62147Sm^{147}_{62}\text{Sm}62147Sm.
A mineral sample contains 4.18 mg4.18 \text{ mg}4.18 mg of 62147Sm^{147}_{62}\text{Sm}62147Sm. Calculate the mass, in grams, of 62147Sm^{147}_{62}\text{Sm}62147Sm that the mineral sample contained when it crystallised 2.84×1092.84 \times 10^92.84×109 years ago. Give your answer to an appropriate number of significant figures.
Calculate the activity, in Bq\text{Bq}Bq, of a sample of 62147Sm^{147}_{62}\text{Sm}62147Sm of mass 4.18 mg4.18 \text{ mg}4.18 mg.
(Take the unified atomic mass unit u=1.661×10−27 kgu = 1.661 \times 10^{-27} \text{ kg}u=1.661×10−27 kg and 1 year=365 days1 \text{ year} = 365 \text{ days}1 year=365 days).
