The activity of a cesium-137 standard produced on December 31, 1960, was calculated for December 31, 1970. With a half-life of 30.17 years, 0.331 half-lives had passed between the two dates. By using the concept of half-lives, the remaining activity was determined to be approximately 4.690 µCi on December 31, 1970.
The activity of a radioactive substance decreases over time due to radioactive decay. In this case, we have a cesium-137 standard that was produced on December 31, 1960, and we want to find its activity on December 31, 1970.
To solve this problem, we need to consider the half-life of cesium-137, which is 30.17 years. The half-life is the time it takes for half of the radioactive substance to decay.
Since the cesium-137 standard was produced on December 31, 1960, we can calculate the number of half-lives that have passed between 1960 and 1970.
To do this, we can subtract the starting year (1960) from the ending year (1970) and divide the result by the half-life:
Number of half-lives = (ending year - starting year) / half-life
= (1970 - 1960) / 30.17
Number of half-lives = 0.331 half-lives
Next, we can use the concept of half-lives to calculate the remaining activity of the cesium-137 standard. Each half-life reduces the activity by half.
So, if the activity of the cesium-137 standard was 5 µCi on December 31, 2007, then after 0.331 half-lives, the activity on December 31, 1970, would be:
Activity on December 31, 1970 = Initial activity * (1/2)^(number of half-lives)
= 5 µCi * (1/2)^(0.331)
= 4.690 µCi
Therefore, the activity of the cesium-137 standard on December 31, 1970, was approximately 4.690 µCi.