A radioisotope has a half-life of 4 days. How much of a 20-gram sample of this radioisotope remains at the end of each time period?
1) 4 days
2) 8 days
half is gone after 4 days, so 1/2 is left or 10 grams
in the next 4 days, half of ten grams is lost so 5 grams is left
Just a word of caution on the wording and me being pedantic. The half life is referring to the original isotope so I like to see the answer referring to this. The mass of the sample may have changed only very slightly.
To calculate how much of a radioisotope remains at the end of each time period, we can use the half-life equation. The equation is:
N = N₀ * (1/2)^(t / T)
Where:
N is the amount of the radioisotope remaining at the end of the time period.
N₀ is the initial amount of the radioisotope.
t is the duration of the time period.
T is the half-life of the radioisotope.
Let's calculate the amount remaining at the end of each time period:
1) 4 days:
N = 20g * (1/2)^(4 / 4) = 10g
2) 8 days:
N = 20g * (1/2)^(8 / 4) = 5g
Therefore, at the end of the 4-day time period, 10 grams of the radioisotope will remain, and at the end of the 8-day time period, 5 grams of the radioisotope will remain.