Cesium 138 has a half life equal to 32.2 minutes. how long will it take for 2/4 of this sample to decay
Note that 2/4 is actually 1/2.
Sra
To determine how long it will take for 2/4 (or 1/2) of the sample to decay, we can use the concept of half-life. The half-life of Cesium 138 is given as 32.2 minutes, meaning every 32.2 minutes, half of the sample will decay and half will remain.
Since you want to calculate the time it takes for half of the sample to decay, we can write the following equation:
Remaining amount = Initial amount * (1/2)^(number of half-lives)
Here, the remaining amount is equal to 2/4 or 1/2 of the initial amount.
1/2 = 1 * (1/2)^(number of half-lives)
To solve for the number of half-lives, we can take the logarithm (with base 1/2) of both sides of the equation:
log base (1/2) (1/2) = log base (1/2) [(1/2)^(number of half-lives)]
1 = number of half-lives * log base (1/2) (1/2)
Since log base (1/2) (1/2) is equal to 1, we have:
1 = number of half-lives
Therefore, it will take one half-life of Cesium 138, which is 32.2 minutes, for 2/4 of the sample to decay.