a sample of radioisotope has a count rate measured by a Muller-Geiger counter of 160 counts per minute. this drop to 20 counts per minute in 1 hour. What is the half life of this source.
3 half lives in 1 hour.
or about 0.333 hours.
To determine the half-life of the radioisotope in question, we can use the count rate measurements and the concept of radioactive decay.
The half-life of a radioactive substance is the time it takes for half of the original quantity of the substance to decay. In this case, the count rate drops from 160 counts per minute to 20 counts per minute in 1 hour, which means it has decreased to 1/8th (20/160) of its original value.
Since the count rate decreases by a factor of 2 each half-life, we can determine the number of half-lives by calculating 1/8 as a power of 2. We'll set up the equation:
(1/2)^(number of half-lives) = 1/8
Taking the logarithm base 2 of both sides of the equation:
log2((1/2)^(number of half-lives)) = log2(1/8)
number of half-lives * log2(1/2) = log2(1/8)
Since log2(1/2) = -1, we have:
number of half-lives * -1 = log2(1/8)
number of half-lives = log2(1/8) * -1
Calculating the value:
number of half-lives = 3
Therefore, the half-life of this radioisotope is 1 hour, as it takes 3 half-lives (each lasting 1 hour) for the count rate to drop to 1/8th of its original value.