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
50 g
d
75 g
c
50 g
To determine how much of element X remains after 10 days, we need to understand what a half-life means. The half-life is the amount of time it takes for half of the radioactive substance to decay.
In this case, the half-life for element X is 5 days. This means that after 5 days, half of the 100-gram sample would have decayed, leaving 50 grams remaining.
Since 10 days have passed (which is twice the length of the half-life), we can calculate the remaining amount. If half of the sample decays every 5 days, after 10 days, another half of the remaining 50 grams would decay.
So, after 10 days, only 25 grams of element X would remain. Therefore, the correct answer is option a) 25 g.
To determine how much of element X remains after 10 days, we need to consider the half-life of the element.
The half-life of element X is given as 5 days. This means that after every 5 days, the amount of element X remaining is halved.
Since 10 days have passed, we can determine the number of half-lives that have occurred within this time period. To do this, we divide the number of days passed (10) by the half-life (5):
10 days / 5 days = 2 half-lives
Since 2 half-lives have occurred, we know that the amount of element X remaining is halved twice. To calculate the amount remaining, we multiply the original amount (100 g) by 1/2 (or 0.5) two times:
Remaining amount = 100 g × (1/2)^2 = 100 g × (1/4) = 25 g
Therefore, option a) 25 g is the correct answer.