Radioactive dating is used for measuring long time intervals of the order of

Options

A. `10^(17)s`
B. `10^7s`
C. `10^(17)years`
D. `10^7 years`

Answer

To solve the question regarding the time intervals that radioactive dating can measure, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Radioactive Dating**:
Radioactive dating is a method used to determine the age of materials, such as rocks or fossils, by measuring the amount of a specific radioactive isotope present in the sample.

2. **Identifying the Isotope Used**:
One of the most commonly used isotopes in radioactive dating is Carbon-14 (C-14). This isotope is particularly useful for dating organic materials.

3. **Time Intervals Measured**:
Radioactive dating can measure time intervals over a wide range. For Carbon-14 dating, it is effective for dating materials that are up to about 50,000 years old. However, other isotopes can be used for much longer time intervals.

4. **Evaluating the Options**:
The question provides several options:
- \(10^{17}\) seconds
- \(10^{7}\) seconds
- \(10^{17}\) years
- \(10^{7}\) years

5. **Converting Time Units**:
To compare the options, we can convert \(10^{17}\) seconds into years:
\[ 10^{17} \text{ seconds} = \frac{10^{17}}{60 \times 60 \times 24 \times 365} \approx 3.17 \times 10^{9} \text{ years} \]
This means \(10^{17}\) seconds is approximately 3.17 billion years, which is a significant time interval.

6. **Conclusion**:
The option that corresponds to the longest time interval that radioactive dating can measure is \(10^{17}\) years. This is because radioactive dating can be used to date geological formations and ancient fossils that are millions to billions of years old.

### Final Answer:
The correct answer is \(10^{17}\) years.

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