Final answer:
To find the remaining amount of a substance after a certain amount of time, use the half-life formula N = N0 (1/2)^(t/T). For a substance with a half-life of 23 hours, after 7 hours a portion of the original amount will remain, determined by raising 1/2 to the exponent t/T and multiplying it by the original amount.
Step-by-step explanation:
The question asks us to calculate how much of a substance with a known half-life remains after a certain period of time that is not a whole number of half-lives. To solve this, we use the principle of radioactive decay, which is often expressed with the formula:
N = N0 (1/2)^(t/T)
Where:
- N is the final amount of the substance,
- N0 is the initial amount of the substance,
- t is the time elapsed,
- T is the half-life of the substance.
In this case, we want to find out what portion of 360kg of a substance with a half-life of 23 hours will remain after 7 hours. Substituting the known values into the equation, we get:
N = 360kg * (1/2)^(7/23)
When we calculate the exponent (7/23), and then raise 1/2 to that power, we get the fraction of the original substance that remains after 7 hours. Finally, we multiply that fraction by the original 360kg to find the remaining mass.