The half life period of a radioactive substance is 140 days. After how much time, 15 g will decay from a 16 g sample of the substance?

Options

A. 140 days
B. 560 days
C. 420 days
D. 280 days

Answer

To solve the problem step by step, we need to determine how long it takes for a 16 g sample of a radioactive substance to decay to 1 g, given that its half-life is 140 days.

### Step-by-Step Solution:

1. **Understand the Half-Life Concept**:
- The half-life of a radioactive substance is the time required for half of the substance to decay. In this case, the half-life is 140 days.

2. **Initial Amount**:
- We start with an initial amount of 16 g of the substance.

3. **Determine the Final Amount**:
- We want to find out how long it takes for the sample to decay to 1 g (since 16 g - 15 g = 1 g).

4. **Calculate the Number of Half-Lives**:
- We will calculate how many half-lives it takes to go from 16 g to 1 g.
- After 1 half-life (140 days):
- 16 g → 8 g
- After 2 half-lives (280 days):
- 8 g → 4 g
- After 3 half-lives (420 days):
- 4 g → 2 g
- After 4 half-lives (560 days):
- 2 g → 1 g

5. **Total Time Calculation**:
- Since it takes 4 half-lives to go from 16 g to 1 g, we multiply the number of half-lives by the duration of each half-life:
\[ \text{Total time} = 4 \times 140 \text{ days} = 560 \text{ days} \]

### Final Answer:
The time required for 15 g to decay from a 16 g sample of the substance is **560 days**.