K-42 has a half-life of 12.4 hours. If you begin with 250g of
K-42, determine how much you will have left after 4 half-lives.
How long does 4 half-lives take?
please help
There is a shorter way, I think, but this is what I would do.
k = 0.693/t1/2
Substitute k into the equation below.
ln(No/N) = kt
No = 250
N = unknown
k from above.
t = time = 4*12.4 = ??
The short way is (n = number of half lives)
1/2^n = fraction left
1/2^4 = ?? and ?? x 250 = xx.
You should get the same answer either way.
To determine how much K-42 you will have left after 4 half-lives, we need to understand what half-life means. The half-life of a substance is the time it takes for half of the substance to decay or transform into another element.
In this case, K-42 has a half-life of 12.4 hours. So, after 12.4 hours, half of the original K-42 will have decayed, and you will have 125g left (half of 250g).
To find out how much K-42 you will have left after 4 half-lives, you can use the formula:
Remaining amount = Initial amount * (0.5 ^ number of half-lives)
Let's calculate the remaining amount after 4 half-lives:
Remaining amount = 250g * (0.5 ^ 4)
Remaining amount = 250g * (0.5 * 0.5 * 0.5 * 0.5)
Remaining amount = 250g * 0.0625
Remaining amount = 15.625g
So, you will have 15.625g of K-42 left after 4 half-lives.
Now, let's determine how long 4 half-lives take. Since we know that each half-life takes 12.4 hours, we can multiply this value by the number of half-lives:
Time for 4 half-lives = 12.4 hours * 4
Time for 4 half-lives = 49.6 hours
Therefore, it takes 49.6 hours for 4 half-lives to complete.