Question

A radioactive substance has a half-life of 5 years. What is the probability that a single atom of this substance will decay within 5 years?

• A. \( \frac{1}{2} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{3}{4} \)
• D. \( \frac{1}{8} \)

Hint:

For radioactive decay, the probability that an atom decays in a given time period is related to the substance's half-life. In each half-life, half of the remaining atoms decay, so the probability of decay within one half-life is always \( \frac{1}{2} \).

Answer 1

The Correct Option is A

Step 1: Understanding the concept of half-life. The half-life of a radioactive substance is the time required for half of the atoms in a sample to decay. In this case, the half-life of the substance is given as 5 years. Step 2: Probability of decay within the half-life. The probability that a single atom will decay within one half-life is 50%, since half of the atoms will have decayed by the end of one half-life. This can be understood using the fact that in each half-life, the number of undecayed atoms reduces to half of the previous amount. Therefore, in a given half-life, the probability of a single atom decaying is: \[ P(\text{decay within 5 years}) = \frac{1}{2} \] Step 3: Conclusion. The probability that a single atom of the radioactive substance will decay within 5 years is \( \frac{1}{2} \). Answer: Therefore, the probability that the atom will decay within 5 years is \( \frac{1}{2} \).