The half life of radioactive isotope is 3 hour. If the initial mass of isotope were 256 g, the mass of it remaining undecayed after 18 hr is a)12 g b)16 g c)4 g d)8 g

Answer

To solve the problem of determining the remaining mass of a radioactive isotope after 18 hours, we can follow these steps:

### Step 1: Identify the half-life and total time
- The half-life of the radioactive isotope is given as 3 hours.
- The total time for which we want to find the remaining mass is 18 hours.

### Step 2: Calculate the number of half-lives
- To find the number of half-lives that have passed in 18 hours, we use the formula:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life time}} = \frac{18 \text{ hours}}{3 \text{ hours}} = 6 \]

### Step 3: Determine the initial mass
- The initial mass of the radioactive isotope is given as 256 grams.

### Step 4: Calculate the remaining mass after each half-life
- After each half-life, the mass of the isotope is halved. We can calculate the remaining mass after each half-life:
- After 1 half-life (3 hours):
\[ \frac{256 \text{ g}}{2} = 128 \text{ g} \]
- After 2 half-lives (6 hours):
\[ \frac{128 \text{ g}}{2} = 64 \text{ g} \]
- After 3 half-lives (9 hours):
\[ \frac{64 \text{ g}}{2} = 32 \text{ g} \]
- After 4 half-lives (12 hours):
\[ \frac{32 \text{ g}}{2} = 16 \text{ g} \]
- After 5 half-lives (15 hours):
\[ \frac{16 \text{ g}}{2} = 8 \text{ g} \]
- After 6 half-lives (18 hours):
\[ \frac{8 \text{ g}}{2} = 4 \text{ g} \]

### Step 5: Conclusion
- After 18 hours, the remaining mass of the radioactive isotope is 4 grams.

Thus, the answer is **c) 4 g**.