how many half lives have passed if only 0.625g remain of the original 40g?
(1/2)^n = .625
n ln(1/2) = ln(.625)
n = .678
makes sense, since one full half-life leave 1/2, which is a bit less than .625
This answer of 0.678 makes no sense to me. By iteration you know that if the sample starts at 40 and ends up at 0.625 it must have gone through six half-lives. Mathematically it is done this way.
2^n = 40/0.625 = 64
n*log 2 = log 64
0.301n = 1.8062
n = 1.8062/0.301 = 6.0
To determine the number of half-lives that have passed, we need to understand the concept of half-life. The half-life is the time it takes for half of a substance to decay or disappear.
In this case, we have 40g of a substance, and only 0.625g remains. This means that 39.375g (40g - 0.625g) has decayed or disappeared.
To find the number of half-lives, we can compare the amount remaining to the original amount after each half-life.
Let's start by calculating the original amount after one half-life:
After one half-life, half of the substance remains. Therefore, the original 40g would become 20g (half of 40g).
Now, let's determine the original amount after two half-lives:
After the first half-life, we had 20g remaining. After the second half-life, half of the remaining 20g will remain. So, we would have 10g (half of 20g) remaining.
Using this pattern, we can continue calculating the original amount after each subsequent half-life until we reach 0.625g.
After three half-lives, we have 5g.
After four half-lives, we have 2.5g.
After five half-lives, we have 1.25g.
After six half-lives, we have 0.625g.
Therefore, it took six half-lives for the original 40g to decay to only 0.625g.