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: Definition of Half-Life. The half-life of a radioactive substance is the duration necessary for half of its atoms to undergo decay. For this specific substance, the half-life is established at 5 years. Step 2: Decay Probability within Half-Life. The likelihood of an individual atom decaying within a single half-life period is 50%. This is a direct consequence of half the atomic sample decaying by the conclusion of this period. This principle is illustrated by the reduction of undecayed atoms by half in each successive half-life. Consequently, the probability of a single atom decaying within a given half-life is: \[P(\text{decay within 5 years}) = \frac{1}{2}\] Step 3: Final Determination. The probability that a singular atom of this radioactive substance will decay within a 5-year interval is \( \frac{1}{2} \). Answer: Accordingly, the probability of the atom decaying within 5 years is \( \frac{1}{2} \).