# The Half Life of Potassium-40

## Understanding Potassium-40 Half Life

Potassium-40 is a radioactive isotope commonly found in rocks and minerals. It undergoes radioactive decay over time, transforming into argon-40. One way to measure the rate of decay is through its half life, which is the time it takes for half of the original sample to decay.

Let's look at an example: A potassium-40 sample starts with 50 atoms, and after 1.25 billion years, there are only 25 atoms left. What is the half life of potassium-40?

## The Calculation

To determine the half life of potassium-40, we can use the formula:

**New amount** = Original amount × (1/2)^n

Where n is the number of half lives. From the data given:

**Original amount** = 50 atoms

**New amount** = 25 atoms

Therefore, we can set up the equation:

25 = 50 × (1/2)^n

Solving for n, we get:

1/2 = (1/2)^n

n = 1

So, the half life of potassium-40 is equivalent to 1 half life, which is 1.25 billion years.

## Conclusion

Therefore, the correct answer is **C. 1.25 years.** Potassium-40 has a half life of 1.25 billion years.

A potassium-40 sample starts with 50 atoms, and 1.25 billion years later, there are 25 atoms. What is the half life of potassium-40? A. 25 years B. 40 years C. 1.25 years D. 2.5 years

Answer: Potassium-40 has a half life of 1.25 billion years. Explanation: New amount = Original amount × (1/2)^n ; where n is the number of half lives. Original amount is 50 atoms and New amount is 25 atoms. Therefore, 25 = 50 × (1/2)^n. Solving for n, we get n = 1. This is equivalent to 1.25 billion years. Therefore, Potassium-40 has a half life of 1.25 billion years. Answer: C