Question

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

Short answer

130 days for one-fourth; 195 days for one-eighth.

Step-by-step solution

Understand the Half-Life Concept

The half-life of a substance is the time it takes for half of the substance to decay. For strontium-85, the half-life is 65 days. This means that every 65 days, the amount of strontium-85 is reduced by half.

Determine the Number of Half-Lives for One-Fourth

To drop to one-fourth of its original level, strontium-85 must go through two half-lives because \(\frac{1}{2} * \frac{1}{2} = \frac{1}{4}\).

Calculate the Time for One-Fourth

Multiply the number of half-lives by the half-life period: \(\text{Time} = 2 \times 65 \text{ days} = 130 \text{ days}\).

Determine the Number of Half-Lives for One-Eighth

To drop to one-eighth of its original level, strontium-85 must go through three half-lives because \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}\).

Calculate the Time for One-Eighth

Multiply the number of half-lives by the half-life period: \(\text{Time} = 3 \times 65 \text{ days} = 195 \text{ days}\).

Key concepts

strontium-85

Strontium-85 is a radioactive isotope commonly used in medical applications, especially for bone scans. It helps in diagnosing bone disorders by highlighting areas of bone growth or repair. This isotope emits gamma rays, which can be detected by imaging equipment to create detailed images of bones.
The choice of strontium-85 is particularly useful because its half-life allows it to remain in the body just long enough to perform diagnostic procedures. Over time, its radiation decreases, minimizing long-term exposure.

• Strontium-85 decays at a predictable rate.
  
• The isotope is effective for detailed bone imaging.
  
• Its usefulness is tied to understanding its half-life and decay process.

radioactive decay

Radioactive decay is the process through which an unstable atomic nucleus loses energy by emitting radiation. This process changes the original atom into a different element or a different isotope of the same element. For strontium-85, decay means that it gradually turns into another, more stable element.
As strontium-85 decays, it emits particles and energy, which can be detected for various applications. The decay follows a specific pattern, known as a decay curve, which helps scientists predict how much of the radioactive material remains at any given time.

• Decay is predictable and measurable.
  
• Different isotopes decay at different rates.
  
• Understanding decay helps in calculating safe usage and disposal.
  

half-life period

The half-life period of a radioactive substance is the time it takes for half of the material to decay. For strontium-85, the half-life is 65 days. This means that in 65 days, half of the original amount of strontium-85 will have decayed, leaving the other half intact.
To determine how long it takes for a substance to decrease to a specific fraction of its original amount, we multiply the number of half-lives needed by the length of one half-life.

• For the radiation level to drop to one-fourth, it takes two half-lives because \(\frac{1}{2} * \frac{1}{2} = \frac{1}{4}\). So, for strontium-85, it takes 130 days (2 \(*\) 65 days).
  
• For the radiation to drop to one-eighth, it takes three half-lives because \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}\). Therefore, it takes 195 days (3 \(*\) 65 days).
  
• Knowing the half-life helps in planning and safety regarding the use and handling of radioactive substances.