To determine how much of the radioactive isotope will be left after 5 half-lives, we can follow these steps:

1. **Understand the concept of half-life**: Each half-life reduces the quantity of the isotope to half of its previous amount.

2. **Initial quantity**: Start with 185 grams of the radioactive isotope.

3. **Calculate the remaining quantity after each half-life**:
- After 1 half-life: $ \frac{185}{2} = 92.5 $ grams
- After 2 half-lives: $ \frac{92.5}{2} = 46.25 $ grams
- After 3 half-lives: $ \frac{46.25}{2} = 23.125 $ grams
- After 4 half-lives: $ \frac{23.125}{2} = 11.5625 $ grams
- After 5 half-lives: $ \frac{11.5625}{2} = 5.78125 $ grams

4. **Final quantity**: After 5 half-lives, 5.78125 grams of the radioactive isotope will be left.

Question

To determine how much of the radioactive isotope will be left after 5 half-lives, we can follow these steps:

1. **Understand the concept of half-life**: Each half-life reduces the quantity of the isotope to half of its previous amount.

2. **Initial quantity**: Start with 185 grams of the radioactive isotope.

3. **Calculate the remaining quantity after each half-life**:
   - After 1 half-life: $ \frac{185}{2} = 92.5 $ grams
   - After 2 half-lives: $ \frac{92.5}{2} = 46.25 $ grams
   - After 3 half-lives: $ \frac{46.25}{2} = 23.125 $ grams
   - After 4 half-lives: $ \frac{23.125}{2} = 11.5625 $ grams
   - After 5 half-lives: $ \frac{11.5625}{2} = 5.78125 $ grams

4. **Final quantity**: After 5 half-lives, 5.78125 grams of the radioactive isotope will be left.

Knowee AI · Accepted Answer

To determine how much of the radioactive isotope will be left after 5 half-lives, we can follow these steps:

1. **Understand the concept of half-life**: Each half-life reduces the quantity of the isotope to half of its previous amount.

2. **Initial quantity**: Start with 185 grams of the radioactive isotope.

3. **Calculate the remaining quantity after each half-life**:
   - After 1 half-life: $ \frac{185}{2} = 92.5 $ grams
   - After 2 half-lives: $ \frac{92.5}{2} = 46.25 $ grams
   - After 3 half-lives: $ \frac{46.25}{2} = 23.125 $ grams
   - After 4 half-lives: $ \frac{23.125}{2} = 11.5625 $ grams
   - After 5 half-lives: $ \frac{11.5625}{2} = 5.78125 $ grams

4. **Final quantity**: After 5 half-lives, 5.78125 grams of the radioactive isotope will be left.

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 185 grams of a radioactive isotope, how much will be left after 5 half-lives?

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