Step-by-step explanation:
To solve this problem, we can use the radioactive decay formula:
N = N₀ * (1/2)^(t/T)
Where:
N₀ = initial amount of substance
N = remaining amount of substance after time t
T = half-life of the substance
We know that the half-life of Pa-231 is 6.75 hours. Therefore, T = 6.75 hours.
After 27.0 hours, the number of half-lives that have passed is 27.0 / 6.75 = 4.
Now, we can use the formula to find the remaining amount of Pa-231:
N = N₀ * (1/2)^(t/T)
N = 150 * (1/2)^(4)
N = 150 * 0.0625
N = 9.375
Therefore, after 27.0 hours, only 9.375 grams of Pa-231 would remain from an initial amount of 150 grams.