To determine the correct formula for calculating the age of a meteorite using its half-life, we need to understand the principle of radioactive decay. The age of a meteorite (or any object with radioactive material) can be calculated using the concept of half-lives, which is the time required for half of the radioactive atoms in a sample to decay.
Let's break down the terminology:
1. Half-life ([tex]\(t_{1/2}\)[/tex]): This is the amount of time it takes for half of the radioactive material to decay.
2. Number of half-lives (n): This refers to how many half-lives have elapsed since the formation of the meteorite or since the start of the decay process.
Given these definitions, the age of the object can be calculated as the product of the number of half-lives and the period of one half-life.
Here's the formula step-by-step:
- Step 1: Determine the half-life ([tex]\( t_{1/2} \)[/tex]) of the radioactive material.
- Step 2: Determine the number of half-lives (n) that have passed.
- Step 3: Multiply the number of half-lives (n) by the half-life ([tex]\( t_{1/2} \)[/tex]).
The formula is:
[tex]\[ \text{Age of object} = n \times t_{1/2} \][/tex]
Hence, the correct formula for calculating the age of a meteorite using its half-life is:
[tex]\[ \text{Age of object} = n \times t_{1/2} \][/tex]
So, the correct answer from the given options is:
[tex]\[ \text{Age of object} = n \times t_{1/2} \][/tex]
