If equal numer of atoms of two radioactive elements are considered, the most dangerous would be the one with a half life of?
a. 4.0 million years b. 100 years
c. 0.01 second d. 1 second

Options

A. a. 4.0 million years
B. b. 100 years
C. c. 0.01 second
D. d. 1 second

Explanation

To determine which radioactive element is the most dangerous based on its half-life, we need to analyze the relationship between half-life and the stability of radioactive isotopes.

**Step 1: Understand Half-Life**
Half-life is the time required for half of the radioactive atoms in a sample to decay. The shorter the half-life, the more unstable the isotope is, and the more radiation it emits in a given period.

**Step 2: Analyze the Options**
We have four options for half-lives:
- a. 4.0 million years
- b. 100 years
- c. 0.01 second
- d. 1 second

**Step 3: Determine Stability**
- A half-life of 4.0 million years indicates a very stable isotope, as it takes a long time for it to decay.
- A half-life of 100 years is still relatively stable but less so than the 4.0 million years.
- A half-life of 1 second is quite short, indicating a higher level of instability and danger.
- A half-life of 0.01 second is extremely short, meaning that the isotope is highly unstable and will emit a significant amount of radiation in a very short time.

**Step 4: Conclusion**
Since we are looking for the most dangerous element, we need to choose the one with the shortest half-life. Among the options, 0.01 second is the shortest half-life, indicating that this isotope is the most unstable and will produce the most radiation.

**Final Answer:**
The most dangerous radioactive element would be the one with a half-life of **c. 0.01 second**.

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