Find the half-life (in hours) of a radioactive substance that is reduced by 10 percent in 5 hours.
.6=e^-.603 (5sec/th)
solve for thalflife.
ln.6=-.693*5/th
th=???
To find the half-life of a radioactive substance, we need to determine the amount of time it takes for the substance to reduce by half.
Given that the substance is reduced by 10 percent in 5 hours, we can calculate the remaining percentage of the substance after 5 hours using the formula:
Remaining percentage = 100% - 10% = 90%
Since we know that the substance has reduced to 90% after 5 hours, we can set up an equation:
Remaining percentage = Initial percentage × (1/2)^(Time / Half-life)
Plugging in the values we have:
90% = 100% × (1/2)^(5 / Half-life)
Simplifying the equation:
0.9 = (1/2)^(5 / Half-life)
To remove the exponent, we will take the logarithm of both sides. Since we want to find the half-life in hours, we'll use the logarithmic base of 2 to find the exponent:
log2(0.9) = (5 / Half-life) × log2(1/2)
Using a calculator to calculate the logarithms, we can find:
-0.1520 = (5 / Half-life) × (-1)
Simplifying further:
0.1520 = 5 / Half-life
To isolate the Half-life on one side, we can rewrite the equation as:
Half-life = 5 / 0.1520
Evaluating this expression:
Half-life ≈ 32.89 hours
Therefore, the half-life of the radioactive substance is approximately 32.89 hours.