Question

you have 979,584 grams of a radioactive kind of argon. if its half - life is 2 hours, how much will be left after 10 hours? grams

Explanation:

Step1: Determine the number of half - lives

The half - life of the radioactive argon is 2 hours, and the total time elapsed is 10 hours. To find the number of half - lives \(n\), we use the formula \(n=\frac{\text{total time}}{\text{half - life}}\). So \(n = \frac{10}{2}=5\).

Step2: Use the radioactive decay formula

The formula for radioactive decay is \(N = N_0\times(\frac{1}{2})^n\), where \(N_0\) is the initial amount of the radioactive substance, \(n\) is the number of half - lives, and \(N\) is the amount remaining after \(n\) half - lives. Here, \(N_0 = 979584\) grams and \(n = 5\). So we calculate \(N=979584\times(\frac{1}{2})^5\).

First, calculate \((\frac{1}{2})^5=\frac{1}{32}\). Then, \(N = 979584\times\frac{1}{32}\).

We can perform the division: \(979584\div32 = 30612\).

Answer:

30612