A 300 gram radioactive sample has life of 3 hour's. After 18 hours, 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 determining the remaining quantity of a radioactive sample after a certain period, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Initial mass of the radioactive sample (N0) = 300 grams
- Half-life (t1/2) = 3 hours
- Total time elapsed (t) = 18 hours

2. **Calculate the Number of Half-Lives:**
- The number of half-lives (n) that have passed can be calculated using the formula:
\[ n = \frac{t}{t_{1/2}} \]
- Substituting the values:
\[ n = \frac{18 \text{ hours}}{3 \text{ hours}} = 6 \]

3. **Apply the Radioactive Decay Formula:**
- The remaining quantity of the radioactive substance after n half-lives can be calculated using the formula:
\[ N_t = N_0 \left(\frac{1}{2}\right)^n \]
- Here, \(N_t\) is the remaining quantity, \(N_0\) is the initial quantity, and \(n\) is the number of half-lives.
- Substituting the known values:
\[ N_t = 300 \text{ grams} \times \left(\frac{1}{2}\right)^6 \]

4. **Calculate the Value of \(\left(\frac{1}{2}\right)^6\):**
- \(\left(\frac{1}{2}\right)^6 = \frac{1}{64}\)

5. **Calculate the Remaining Quantity:**
- Now substituting back into the equation:
\[ N_t = 300 \text{ grams} \times \frac{1}{64} = \frac{300}{64} \text{ grams} \]
- Performing the division:
\[ N_t = 4.6875 \text{ grams} \]

6. **Round Off the Result:**
- Rounding 4.6875 grams gives approximately 4.68 grams.

### Final Answer:
After 18 hours, the remaining quantity of the radioactive sample will be approximately **4.68 grams**.

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