Potassium-42 has a half-life of 12.4 hours. How much of a 1600g sample of potassium-42 will be left after 36.0 hours?
m = mi e^- k t
1/2 = e^-k *12.4
ln 0.5 = -12.4 k
k = -.693 / -12.4 = .0559
so
m = 1600 e^-.0559*36
= 1600 (.134) = 214
check in head
36 hours is about 3 half lives
so about 1/8 of original
so around 200, ok
1600 * (1/2)^(36.0 / 12.4)
To find out how much of the potassium-42 sample will be left after 36.0 hours, we can use the concept of half-life.
Step 1: Determine the number of half-lives passed.
Since the half-life of potassium-42 is 12.4 hours, we need to calculate the number of half-lives that have occurred during the 36.0 hours.
Number of half-lives = time elapsed / half-life
Number of half-lives = 36.0 hours / 12.4 hours per half-life
Number of half-lives ≈ 2.9032 half-lives (rounded to four decimal places)
Step 2: Calculate the remaining fraction of the sample.
Since potassium-42 undergoes radioactive decay, the remaining fraction can be determined by raising 0.5 (representing half of the substance) to the power of the number of half-lives passed.
Remaining fraction = (0.5)^(number of half-lives)
Remaining fraction = (0.5)^2.9032 (using the rounded value)
Step 3: Calculate the remaining mass of the sample.
To find the remaining mass, multiply the remaining fraction by the initial mass of the sample.
Remaining mass = remaining fraction × initial mass
Remaining mass = (0.5)^2.9032 × 1600g (using the given initial mass of 1600g)
Using a calculator or computer program, we can calculate the approximate remaining mass of the sample by plugging in the numbers from the previous steps.
Remaining mass ≈ 135.6187g
Therefore, approximately 135.6187 grams of the 1600g potassium-42 sample will be left after 36.0 hours.