Half-life of a radioactive substance is 120 days. After 480 days, 4 g will be reduced to

Options

A. 2
B. 1
C. 0.5
D. 0.25

Explanation

To solve the problem of how much of a radioactive substance remains after a certain period, we can use the concept of half-life.

### Step-by-Step Solution:

1. **Identify the half-life and total time:**
- The half-life (T_half) of the radioactive substance is given as 120 days.
- The total time (t) after which we want to find the remaining quantity is 480 days.

2. **Calculate the number of half-lives:**
- To find out how many half-lives fit into 480 days, we divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{t}{T_{half}} = \frac{480 \text{ days}}{120 \text{ days}} = 4 \]
- This means that 480 days is equivalent to 4 half-lives.

3. **Determine the initial amount:**
- The initial amount (A_0) of the substance is given as 4 grams.

4. **Calculate the remaining amount after each half-life:**
- After the first half-life (120 days), the amount remaining is:
\[ A_1 = \frac{A_0}{2} = \frac{4 \text{ g}}{2} = 2 \text{ g} \]
- After the second half-life (240 days), the amount remaining is:
\[ A_2 = \frac{A_1}{2} = \frac{2 \text{ g}}{2} = 1 \text{ g} \]
- After the third half-life (360 days), the amount remaining is:
\[ A_3 = \frac{A_2}{2} = \frac{1 \text{ g}}{2} = 0.5 \text{ g} \]
- After the fourth half-life (480 days), the amount remaining is:
\[ A_4 = \frac{A_3}{2} = \frac{0.5 \text{ g}}{2} = 0.25 \text{ g} \]

5. **Final Result:**
- After 480 days, the remaining amount of the radioactive substance is **0.25 grams**.

### Summary of Calculation:
- Initial amount: 4 g
- After 1 half-life (120 days): 2 g
- After 2 half-lives (240 days): 1 g
- After 3 half-lives (360 days): 0.5 g
- After 4 half-lives (480 days): 0.25 g

### Final Answer:
**0.25 grams**

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