The half life of a radioactive isotope is 4 hours. If the initial mass of the isotope were 25 g, the mass of it remaining undecayed after 12 hours would be:

Options

A. 8g
B. 3g
C. 6g
D. 10g

Explanation

To solve the problem of determining the remaining mass of a radioactive isotope after a certain period, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Half-life of the isotope (t_half) = 4 hours
- Initial mass of the isotope (N_0) = 25 g
- Total time elapsed (t) = 12 hours

2. **Calculate the Number of Half-Lives (n):**
- The number of half-lives can be calculated using the formula:
\[ n = \frac{t}{t_{half}} \]
- Substituting the values:
\[ n = \frac{12 \text{ hours}}{4 \text{ hours}} = 3 \]
- Thus, there are 3 half-lives in 12 hours.

3. **Calculate the Remaining Mass of the Isotope (N_t):**
- The remaining mass after n half-lives can be calculated using the formula:
\[ N_t = N_0 \left(\frac{1}{2}\right)^n \]
- Substituting the values:
\[ N_t = 25 \text{ g} \left(\frac{1}{2}\right)^3 \]
- Calculate \(\left(\frac{1}{2}\right)^3\):
\[ \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]
- Now, substituting this back:
\[ N_t = 25 \text{ g} \times \frac{1}{8} = \frac{25}{8} \text{ g} = 3.125 \text{ g} \]

4. **Final Result:**
- The mass of the radioactive isotope remaining undecayed after 12 hours is approximately 3.125 g.

### Summary:
The mass of the radioactive isotope remaining undecayed after 12 hours is **3.125 g**.