The half-life for a 100-gram sample of radioactive element X is 10 days. How much of element X remains after 30 days have passed?
a
75 g
b
50 g
c
12.5 g
d
25 g
After 10 days, half of the sample remains, so 100 grams * 1/2 = <<100*1/2=50>>50 grams remain.
After another 10 days, half of the remaining sample remains, so 50 grams * 1/2 = <<50*1/2=25>>25 grams remain.
After another 10 days, half of the remaining sample remains, so 25 grams * 1/2 = <<25*1/2=12.5>>12.5 grams remain.
Therefore, the answer is c) 12.5 g.
To find out how much of element X remains after 30 days have passed, we can use the formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Plugging in the given values, the formula becomes:
Amount remaining = 100 g * (1/2)^(30 days / 10 days)
Simplifying this, we have:
Amount remaining = 100 g * (1/2)^3
Since (1/2)^3 is equal to 1/8, we get:
Amount remaining = 100 g * 1/8
Therefore, the amount of element X that remains after 30 days is:
Amount remaining = 100 g * 1/8 = 12.5 g
So, the answer is option c) 12.5 g.
To determine how much of element X remains after 30 days, we need to understand what half-life means. The half-life of a radioactive substance is the time it takes for half of the sample to decay.
In this case, the half-life of element X is 10 days. This means that every 10 days, half of the original sample will decay.
After 10 days, 50 grams of element X will remain (half of the original 100 grams).
After another 10 days (20 days in total), 25 grams of element X will remain (half of the remaining 50 grams).
Therefore, after 30 days, the answer is option d) 25 g.