A 300 gram radioactive sample has life of 3 hour's After 18 hour's remaining quantity will be:

Options

A. 4.68 gram
B. 2.34 gram
C. 3.34 gram
D. 9.37 gram

Answer

To solve the problem of finding the remaining quantity of a radioactive sample after a certain period, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Quantity (n0)**:
The initial quantity of the radioactive sample is given as:
\[ n_0 = 300 \text{ grams} \]

2. **Identify the Half-Life (t_half)**:
The half-life of the radioactive sample is given as:
\[ t_{half} = 3 \text{ hours} \]

3. **Determine the Total Time (t)**:
We need to calculate the remaining quantity after:
\[ t = 18 \text{ hours} \]

4. **Calculate the Number of Half-Lives (n)**:
The number of half-lives that have passed can be calculated using the formula:
\[ n = \frac{t}{t_{half}} = \frac{18 \text{ hours}}{3 \text{ hours}} = 6 \]

5. **Use the Formula for Remaining Quantity (n_t)**:
The remaining quantity of the radioactive sample after time \( t \) can be calculated using the formula:
\[ n_t = n_0 \left( \frac{1}{2} \right)^n \]
Substituting the values we have:
\[ n_t = 300 \left( \frac{1}{2} \right)^6 \]

6. **Calculate \( \left( \frac{1}{2} \right)^6 \)**:
\[ \left( \frac{1}{2} \right)^6 = \frac{1}{64} \]

7. **Calculate Remaining Quantity**:
Now substituting back into the equation:
\[ n_t = 300 \times \frac{1}{64} = \frac{300}{64} \approx 4.6875 \text{ grams} \]

8. **Final Result**:
Rounding to two decimal places, the remaining quantity after 18 hours is approximately:
\[ n_t \approx 4.69 \text{ grams} \]

### Final Answer:
The remaining quantity after 18 hours will be approximately **4.69 grams**.