Half Life / Alpha Decay Question - No IDea

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To determine the age of a space rock containing 3.20 g of 147Sm and 0.110 g of 143Nd, the decay of samarium to neodymium must be analyzed using the half-life of 1.06 x 10^11 years. The calculation assumes that the rock originally contained only samarium, with the neodymium being a product of alpha decay. The decay formula can be applied to estimate the age based on the current amounts of each isotope. It is noted that the mass loss from emitted alpha particles is negligible due to the small fraction of neodymium present. This approach provides a method to estimate the rock's age accurately.
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Half Life / Alpha Decay Question -- No IDea

Homework Statement



A space rock contains 3.20 g of 147 62 Sm and 0.110 g of 143 60 Nd. 147 62 Sm alpha decays to 143 60 Nd with a half-life of 1.06 1011 yr. If the rock originally contained no , how old is it?

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The Attempt at a Solution



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If you presume that it was all samarium with no neodymium, then all you need to do is apply the decay formula to the original sample as though all the mass was samarium. (Now it's true that the alpha particles emitted represent a loss of mass, but I'd think since the neodymium is a minor fraction of the samarium you can ignore the loss.)
 
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