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
75 g
b
25 g
c
50 g
d
100 g
The half-life for element X is 5 days. This means that after 5 days, half of the sample will decay and the remaining half will still remain.
After 5 days: 100 g / 2 = 50 g remaining
After another 5 days (total of 10 days): 50 g / 2 = 25 g remaining
Therefore, after 10 days have passed, 25 grams of element X remains.
The answer is (b) 25 g.
The half-life of an element is the time it takes for half of the original sample to decay. In this case, the half-life of element X is 5 days.
After 5 days, half of the sample will have decayed. So, after 5 days, we will have 100g / 2 = 50g remaining.
Since another 5 days have passed (for a total of 10 days), we can calculate how much of the remaining sample will decay.
Since the half-life is 5 days, it takes two half-lives (5 days x 2) for the sample to decay completely.
So, after 10 days, another half-life has passed, and half of the remaining 50g will decay.
Therefore, after 10 days, we will have 50g / 2 = 25g of element X remaining.
Therefore, the answer is b) 25g.
To calculate how much of element X remains after 10 days have passed, we need to consider the concept of half-life. The half-life is the time it takes for half of the radioactive material to decay.
In this case, the half-life of element X is 5 days. This means that every 5 days, the amount of element X will decrease by half.
After 5 days, half of the 100-gram sample will remain, which is 50 grams. Now, we need to calculate the remaining amount after an additional 5 days (total of 10 days).
Since the original half-life was 5 days, we divide the remaining time (10 days) by the half-life to determine the number of times the half-life is completed:
10 days / 5 days = 2 times
Since the half-life has been completed twice, the remaining amount will be reduced by half twice.
Starting with 50 grams remaining after the first 5 days, we take half of it:
50 grams / 2 = 25 grams
Then we take half of the remaining 25 grams:
25 grams / 2 = 12.5 grams
Therefore, after 10 days have passed, a 100-gram sample of element X will have approximately 12.5 grams remaining.
The correct answer is b) 25 grams.