To determine how much of the radioactive isotope will be left after 4 half-lives, we can follow these steps:

1. **Identify the initial mass**: The initial mass of the radioactive isotope is 175 grams.

2. **Understand the concept of half-life**: After each half-life, the remaining quantity of the isotope is reduced to half of its previous amount.

3. **Calculate the remaining mass after each half-life**:
- After the 1st half-life:
$$
\text{Remaining mass} = \frac{175}{2} = 87.5 \text{ grams}
$$
- After the 2nd half-life:
$$
\text{Remaining mass} = \frac{87.5}{2} = 43.75 \text{ grams}
$$
- After the 3rd half-life:
$$
\text{Remaining mass} = \frac{43.75}{2} = 21.875 \text{ grams}
$$
- After the 4th half-life:
$$
\text{Remaining mass} = \frac{21.875}{2} = 10.9375 \text{ grams}
$$

4. **Conclusion**: After 4 half-lives, the remaining mass of the radioactive isotope will be 10.9375 grams.

Question

To determine how much of the radioactive isotope will be left after 4 half-lives, we can follow these steps:

1. **Identify the initial mass**: The initial mass of the radioactive isotope is 175 grams.

2. **Understand the concept of half-life**: After each half-life, the remaining quantity of the isotope is reduced to half of its previous amount.

3. **Calculate the remaining mass after each half-life**:
   - After the 1st half-life: 
     $$
     \text{Remaining mass} = \frac{175}{2} = 87.5 \text{ grams}
     $$
   - After the 2nd half-life: 
     $$
     \text{Remaining mass} = \frac{87.5}{2} = 43.75 \text{ grams}
     $$
   - After the 3rd half-life: 
     $$
     \text{Remaining mass} = \frac{43.75}{2} = 21.875 \text{ grams}
     $$
   - After the 4th half-life: 
     $$
     \text{Remaining mass} = \frac{21.875}{2} = 10.9375 \text{ grams}
     $$

4. **Conclusion**: After 4 half-lives, the remaining mass of the radioactive isotope will be 10.9375 grams.

Knowee AI · Accepted Answer

To determine how much of the radioactive isotope will be left after 4 half-lives, we can follow these steps:

1. **Identify the initial mass**: The initial mass of the radioactive isotope is 175 grams.

2. **Understand the concept of half-life**: After each half-life, the remaining quantity of the isotope is reduced to half of its previous amount.

3. **Calculate the remaining mass after each half-life**:
   - After the 1st half-life: 
     $$
     \text{Remaining mass} = \frac{175}{2} = 87.5 \text{ grams}
     $$
   - After the 2nd half-life: 
     $$
     \text{Remaining mass} = \frac{87.5}{2} = 43.75 \text{ grams}
     $$
   - After the 3rd half-life: 
     $$
     \text{Remaining mass} = \frac{43.75}{2} = 21.875 \text{ grams}
     $$
   - After the 4th half-life: 
     $$
     \text{Remaining mass} = \frac{21.875}{2} = 10.9375 \text{ grams}
     $$

4. **Conclusion**: After 4 half-lives, the remaining mass of the radioactive isotope will be 10.9375 grams.

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 175 grams of a radioactive isotope, how much will be left after 4 half-lives?

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