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
50 g
d
100 g
c. 50 g
The half-life of a radioactive substance is the amount of time it takes for half of the sample to decay. In this case, the half-life of element X is 5 days.
After 5 days, half of the sample will remain, so we can calculate:
100 g / 2 = 50 g
Now, after another 5 days (a total of 10 days), another half of the remaining sample will decay.
50 g / 2 = 25 g
Therefore, after 10 days have passed, 25 grams of element X will remain.
The correct answer is (a) 25 g.
To calculate how much of element X remains after 10 days have passed, you need to know the half-life of element X. The half-life is the time it takes for half of a sample of radioactive material to decay.
In this case, the half-life of element X is given as 5 days. This means that after every 5 days, half of the remaining sample will decay.
To calculate how much remains after 10 days, we can divide the time (10 days) by the half-life (5 days) to determine how many half-lives have occurred. In this case, 10 divided by 5 equals 2 half-lives.
Since each half-life reduces the sample by half, after two half-lives, the remaining sample will be reduced by (1/2)*(1/2) or (1/4) of the original amount.
So, if you started with 100 grams of element X, after two half-lives (which is 10 days in this case), the remaining amount will be (1/4) of the original amount.
100 grams * (1/4) = 25 grams
Therefore, the correct answer is option a) 25 grams.