Question

"How much of a 80 g sample of 1-131 atoms will remain after 3 half lives?

Answer 1

Main Answer:

After 3 half-lives, approximately 10 g of the 80 g sample of 1-131 atoms will remain.

Explanation:

The decay of radioactive isotopes follows an exponential decay model. In each half-life, half of the radioactive atoms decay. Therefore, after the first half-life, 40 g remains; after the second, 20 g remains; and after the third, 10 g remains. This pattern can be expressed mathematically as
`\( N_t = N_0 * (1/2)^t \), where \( N_t \)` is the remaining quantity after time
`\( t \), \( N_0 \)` is the initial quantity, and
`\( t \)` is the number of half-lives.

In the case of the 80 g sample of 1-131 atoms, the initial quantity
`(\( N_0 \))` is 80 g. After the first half-life
`(\( t = 1 \)), \( N_t = 80 * (1/2) = 40 \) g.` After the second half-life
`(\( t = 2 \)), \( N_t = 40 * (1/2) = 20 \) g.` Finally, after the third half-life
`(\( t = 3 \)), \( N_t = 20 * (1/2) = 10 \) g.`

This means that after 3 half-lives, only 10 g of the initial 80 g sample of 1-131 atoms will remain. The exponential decay model is a fundamental concept in nuclear physics and is crucial for understanding the behavior of radioactive substances over time.