A space rock contains 3.00 g of 62^147 Sm and 0.150 g of 60^143 Nd. 62^147 Sm decays to 60^1

step 1 First writing the atomic mass of atomic mass of 14762 SM, which is equal to 146 .9 .9 .U. multip

A space rock contains 3.00 g of 62^147 Sm and 0.150 g of ...

A space rock contains $3.00 \mathrm{g}$ of ${ }_{62}^{147} \mathrm{Sm}$ and $0.150 \mathrm{g}$ of ${ }_{60}^{143} \mathrm{Nd}$. ${ }_{62}^{147} \mathrm{Sm}$ decays to ${ }_{60}^{143} \mathrm{Nd}$ with a half-life of $1.06 \times 10^{11}$ yr. If the rock originally contained no ${ }_{60}^{143} \mathrm{Nd}$ how old is it?

Key Concepts

Parent-Daughter Ratio in Radiometric Dating

Radiometric dating uses the ratio of parent (radioactive) to daughter (decay product) isotopes to estimate the age of a sample. When the original amount of daughter isotope is known or assumed to be zero, the measured quantities of both parent and daughter can be used alongside the decay law to calculate the elapsed time since the formation of the sample.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a given nucleus will decay. It provides a direct measure of the rate at which a radioactive isotope undergoes decay and is intrinsically connected to the half-life. Knowledge of the decay constant is essential for accurately computing ages using the principles of radioactive decay.

Half-Life

Half-life is the time required for half of a sample of a radioactive isotope to decay. It is a fundamental characteristic of each radioactive element and is related to the decay constant by the equation t?/? = ln(2)/?. The concept of half-life is crucial in determining the age of an object by assessing the ratio of remaining parent isotopes to produced daughter isotopes.

Radioactive Decay Law

The radioactive decay law describes how unstable nuclei lose energy by emitting radiation over time. This decay follows an exponential behavior, represented mathematically as N(t) = N?e^(–?t), where N? is the original amount of the isotope, N(t) is the remaining amount at time t, and ? is the decay constant. This principle underpins many dating techniques in both geological and astronomical contexts.

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