Ba has a half-life of 283.2 hours. How long would it take for the 50 mg of Ba in a sample to decay to 1.0 mg?
50 * (1/2)^n = 1 ???
.5^n = .02
n ln .5 = ln .02 (any base log will do)
n = ln(.02) / ln(.5)
then n * 283.2
isnt it..
1=50(.5)^(x/283.2)
1/50=(.5)^(x/283.2)
logbase.5(1/50)=x/283.2
x=1598.34
s=k ln W * / g!^¥ + ([x:86:23]<€{fn t})
what does this means?
It means you are trying to win the lotto from a useless formula that some blokes made up to have a fun time... Fun time of what you ask? Fun time at laughing at alllll the people who believe this BS...
To calculate the time it takes for a sample of Ba to decay from 50 mg to 1.0 mg, we can use the concept of half-life.
The half-life of a radioactive substance, such as Ba, is the time it takes for half of the original amount to decay. In this case, we are given that the half-life of Ba is 283.2 hours.
Since we want to know the time it takes for the sample to decay from 50 mg to 1.0 mg, we can assume that the remaining 1.0 mg is half of the original amount (50 mg).
Now, let's break down the calculation:
1. Calculate how many half-lives are needed for the decay:
Since each half-life reduces the amount by half, we need to find how many times we can divide 50 mg by 2 until we reach 1.0 mg.
50 mg ÷ 2 = 25 mg ÷ 2 = 12.5 mg ÷ 2 = 6.25 mg ÷ 2 = 3.125 mg ÷ 2 = 1.5625 mg ÷ 2 ≈ 0.78125 mg ÷ 2 ≈ 0.390625 mg ÷ 2 ≈ 0.1953125 mg ÷ 2 ≈ 0.09765625 mg
It took 10 divisions by 2 to reach approximately 0.09765625 mg. So, 10 half-lives are needed for the decay.
2. Calculate the time it takes for the decay:
Since each half-life is 283.2 hours, we can multiply the half-lives by the half-life duration:
10 half-lives × 283.2 hours/half-life = 2,832 hours
So, it would take approximately 2,832 hours for 50 mg of Ba to decay to 1.0 mg.
Remember to note that the calculation is an approximation, and actual decay may vary slightly due to experimental factors.