Examine the information.
Isotope B has a half-life of 3 days. A scientist measures out 100 grams of this substance. After 6 days has passed, the scientist reexamines the sample.
How much of Isotope B will remain in the sample?
100 grams
63 grams
94 grams
25 grams
25
The half life is 3 days. You start with 100 g. So at the end of 3 days, 1/2 of it is gone and you're left with 50 g.
At the end of another 3 days, another half is gone. What's left.
right
To determine how much of Isotope B will remain in the sample after 6 days, we need to use the concept of the half-life.
The half-life of an isotope is the time it takes for half of the initial amount of the isotope to decay. In this case, Isotope B has a half-life of 3 days.
To calculate the amount remaining after a given time, we can use the formula:
Amount Remaining = Initial Amount * (1/2)^(time elapsed / half-life)
In this case, the initial amount is 100 grams, and the time elapsed is 6 days. Plugging these values into the formula:
Amount Remaining = 100 * (1/2)^(6 / 3)
Simplifying:
Amount Remaining = 100 * (1/2)^2
Calculating the exponent:
Amount Remaining = 100 * (1/2)^2
Amount Remaining = 100 * (1/4)
Amount Remaining = 25 grams
Therefore, after 6 days, only 25 grams of Isotope B will remain in the sample.