`x g` of a radioactive substance will be decomposed to `7//8x g` in `40 s` if the half-life periof is `10 s`. T or F

Answer

To determine whether the statement is true or false, we need to analyze the decay of a radioactive substance over time given its half-life.

### Step-by-Step Solution:

1. **Identify the Initial Amount**:
- Let the initial amount of the radioactive substance be \( x \) grams.

2. **Understand Half-Life**:
- The half-life of the substance is given as 10 seconds. This means that every 10 seconds, half of the remaining substance will decay.

3. **Calculate the Amount After Each Half-Life**:
- After 10 seconds (1 half-life), the amount remaining will be:
\[ \text{Remaining} = \frac{x}{2} \]
- After 20 seconds (2 half-lives), the amount remaining will be:
\[ \text{Remaining} = \frac{x}{4} \]
- After 30 seconds (3 half-lives), the amount remaining will be:
\[ \text{Remaining} = \frac{x}{8} \]
- After 40 seconds (4 half-lives), the amount remaining will be:
\[ \text{Remaining} = \frac{x}{16} \]

4. **Calculate the Decomposed Amount**:
- The amount that has decomposed after 40 seconds is:
\[ \text{Decomposed} = x - \frac{x}{16} = \frac{16x}{16} - \frac{x}{16} = \frac{15x}{16} \]

5. **Compare with Given Statement**:
- The problem states that the remaining amount is \( \frac{7}{8}x \).
- To compare, convert \( \frac{7}{8} \) to a fraction with a denominator of 16:
\[ \frac{7}{8} = \frac{14}{16} \]
- We found that the remaining amount is \( \frac{x}{16} \), which is not equal to \( \frac{14}{16}x \).

6. **Conclusion**:
- Since \( \frac{15}{16}x \) (the decomposed amount) does not equal \( \frac{7}{8}x \), the statement is **False**.

### Final Answer:
**False**