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
100 g
c
75 g
d
50 gg
c
75 g
To determine how much of element X remains after 10 days have passed, we need to consider its half-life.
A half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of element X is given as 5 days.
Given that 10 days have passed, we can divide the time by the half-life to determine how many half-lives have elapsed. In this case, 10 divided by 5 gives us 2 half-lives.
Each half-life results in half of the substance decaying. So, after 1 half-life has passed (5 days in this case), 50% of the radioactive element X remains. After 2 half-lives (10 days in this case), 50% of the remaining 50% will decay, leaving us with 25% of the original amount.
Therefore, the correct answer is option a) 25 g.
To find out how much of element X remains after 10 days, we need to calculate the number of half-lives that have passed.
Half-life is the time it takes for half of a radioactive substance to decay.
Given that the half-life of element X is 5 days, after 5 days, 50 grams of the sample will remain. This is one half-life.
After another 5 days, which is a total of 10 days, another half-life has passed. So, another half of the remaining 50 grams will decay.
Therefore, after 10 days, there will be 25 grams of element X remaining.
So, the correct answer is:
a) 25 g