The half-life for a 100-gram sample of radioactive element X is 5 days. How much of element X remains after 10 days have passed?
a
25 g
b
75 g
c
100 g
d
50 g
The half-life of element X is 5 days, which means that every 5 days, the amount of element X will be reduced by half.
After 5 days, there will be 50 grams of element X remaining (half of the original 100 grams).
After another 5 days (10 days total), the remaining 50 grams will be reduced by half again, leaving 25 grams of element X remaining.
Therefore, the answer is 25 grams.
The correct option is a) 25 g.
To calculate how much of element X remains after 10 days, we need to determine how many half-lives have passed and then calculate the remaining amount.
Given that the half-life of element X is 5 days, we can divide 10 days by the half-life to find the number of half-lives that have occurred.
10 days / 5 days = 2 half-lives
Each half-life reduces the amount of element X by half, so after 2 half-lives, the remaining amount is:
100 g * (1/2) * (1/2) = 25 g
Therefore, the correct answer is option a) 25 g.
To determine how much of element X remains after 10 days, we need to understand the concept of a half-life.
The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay or disintegrate. In this case, the half-life of element X is 5 days.
After the first half-life (5 days), half of the original sample will remain. Therefore, after 5 days, the 100-gram sample will have decreased to 50 grams.
After another 5 days (the second half-life), half of the remaining 50 grams will decay, leaving only 25 grams.
Therefore, the answer is option A: 25 g.