Strontium-85, used for bone scans, has a half-life of 65 days.
b. How long will it take for the radiation level of strontium-85 to drop to one-eighth of its original level?

Verified step by step guidance

1. Understand the concept of half-life: The half-life of a radioactive isotope is the time it takes for half of the radioactive substance to decay. In this case, the half-life of strontium-85 is 65 days.
2. Determine the fraction of the original radiation level remaining: The problem states that the radiation level drops to one-eighth (\( \frac{1}{8} \)) of its original level. This corresponds to three half-lives because \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \).
3. Calculate the total time required for three half-lives: Multiply the number of half-lives (3) by the half-life duration (65 days). Use the formula \( \text{Total Time} = \text{Number of Half-Lives} \times \text{Half-Life Duration} \).
4. Substitute the values into the formula: \( \text{Total Time} = 3 \times 65 \). Perform the multiplication to find the total time.
5. Interpret the result: The total time calculated represents how long it will take for the radiation level of strontium-85 to drop to one-eighth of its original level.

Key Concepts

Half-Life

Half-life is the time required for a quantity to reduce to half its initial value. In the context of radioactive isotopes like strontium-85, it indicates how quickly the substance decays. For strontium-85, the half-life is 65 days, meaning after this period, only half of the original amount remains.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. In radioactive decay, this means that the amount of substance decreases rapidly at first and then more slowly over time. The formula used to calculate the remaining quantity after a certain time involves the initial amount and the number of half-lives that have passed.

Fractional Reduction

Fractional reduction refers to the proportion of the original quantity that remains after a certain number of half-lives. To reach one-eighth of the original level, the substance must undergo three half-lives, as each half-life reduces the amount by half: after one half-life, 1/2 remains; after two, 1/4; and after three, 1/8.