# Write an equation for the decay of potassium 40 to argon 40 decay

## Which of the following reactions corresponds to the potassium-40 decay?

In a sample of rock that does not contain appreciable amounts of Pb, the most abundant isotope of lead, we can assume that lead was not present when the rock was formed. So that's this numerator over here. Since first-order reactions have already been covered in detail in the kinetics chapter, we will now apply those concepts to nuclear decay reactions. Consequently, the n:p ratio is decreased, and the daughter nuclide lies closer to the band of stability than did the parent nuclide. Other methods, such as rubidium-strontium dating Rb decays into Sr with a half-life of So the whole point of this-- I know the math was a little bit involved, but it's something that you would actually see in a pre-calculus class or an algebra 2 class when you're studying exponential growth and decay. Potassium-argon dating uses a similar method. How can potassium 40 simultaneously have too many of both? And then, to solve for k, we can divide both sides by negative 1. So let's take the natural log of our previous answer.

As the outer electron drops into the vacancy, it will emit energy. And then, to solve for k, we can divide both sides by negative 1.

Figure 5. It might be 1 gram, kilogram, 5 grams-- whatever it might be-- whatever we start with, we take e to the negative k times 1. Present day estimates for the age of the Earth's crust from this method is at 4 billion years.

Along with uranium and thorium, potassium contributes to the natural radioactivity of rocks and hence to the Earth heat. And I closed both parentheses. If a rock sample is crushed and the amount of Ar gas that escapes is measured, determination of the ArK ratio yields the age of the rock.

### Potassium-40 beta decay equation

And what we can do is we can multiply the negative times the top. And now, we can get our calculator out and just solve for what this time is. How do we figure out how old this sample is right over there? Image used with permission CC-BY 4. Summary and Vocabulary The half-life of an isotope is used to describe the rate at which the isotope will decay and give off radiation. We know, after that long, that half of the sample will be left. When the organism dies, this consumption stops, and no new carbon is added to the organism. And usually, these aren't measured directly, and you really care about the relative amounts. And, you know, Sal, gave this very high-level explanation, and then, you say, oh, well, there must be some super difficult mathematics after that. But let's say you were able to figure out the potassium is 1 milligram.

Interactive Simulation: Visualizing Half-Life Click on this interactive simulation to visualize what happens to a radioisotope when it decays. At that moment, the rock contains a certain amount of potassium but no argon.

Radioactive Half-Lives Radioactive decay follows first-order kinetics. We're just dividing both sides of this equation by negative k.

## Radioactive decay

So let's say we start with N0, whatever that might be. The loss of an inner shell electron leaves a vacancy that will be filled by one of the outer electrons. Electron capture has the same effect on the nucleus as does positron emission: The atomic number is decreased by one and the mass number does not change. This is as expected for a process following first-order kinetics. Since U has a half-life of 4. And now, we can get our calculator out and just solve for what this time is. Example 1 decays with a half-life of 5. For example: the half-life of is 1.

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