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

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

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This process results in the transmutation of elements, whereby the original (parent) isotope transforms into a daughter isotope over time.

Half-Life

The half-life of a radioactive isotope is the time required for half of the initial amount of the isotope to decay. It is a key property of radioactive materials and is used to quantify the rate at which decay occurs, providing the basis for calculating the decay constant with the relation ? = ln(2)/half-life.

Radiometric Dating

Radiometric dating is a technique used to determine the age of materials based on the decay rates of radioactive isotopes. By measuring the ratio of remaining parent isotopes to the accumulated daughter isotopes and applying decay equations, one can estimate the elapsed time since the formation of the material.

Exponential Decay Equation

The exponential decay equation, N = N?e^(??t), describes the mathematical relationship governing radioactive decay. Here, N is the quantity of the parent isotope remaining after time t, N? is the original amount, and ? is the decay constant. This equation is fundamental in modeling decay processes and calculating the age of samples.

Transcript

00:01 In this question, we are basically looking at dating of a particular space rock, but looking at contents.

00:11 Right? and we know that for the, we are given that the rock initially is made up of completely samaria, right? samaria 147.

00:25 Right, let me just label that as red.

00:28 And right now, after a certain period of time, which we don't know, some of the cemirium, right, has decayed.

00:44 Right, and we are left with some samarium with neodynium.

00:52 Right? there's this blue part which is the neodynium.

01:00 Right, so this is, this is the samarium.

01:08 You want to find, and we are given quite specifically, that this is, this is, three grams and this is one 0 .15 .150 grams now we know that the decay right the decay from samarium to neodynium is 1 is to 1 so one samarium nuclei will decay into 1 niodinium so actually we expect that the total number of cimmerm will simply be the total number of samarium now plus the number of neodynium.

02:06 Right and to calculate what is the age, we know the half -life, right? we are given that the half -life of cemirium is actually 1 .06 times 10 to power of 11 years.

02:35 So what we can do is we find out what is the number of neutinium molecules in 0 .150 grams.

02:47 We find out what is the number of cemaria molecules in 3 grams then we look at what is the total number of cimmerium right so we find what is number of dinaway 0 .150 grams then we find total total samarium initially at the start right at the start initial...

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