SOLUTION: I have this chart that talks about the half life of these and they are all different. I am not really understanding what the concept is here. How do I even attempt to answer this q

Question 380265: I have this chart that talks about the half life of these and they are all different. I am not really understanding what the concept is here. How do I even attempt to answer this question...I don't even understand. I looked up half-life and it just doesn't make sense. Please explain and help me solve this problem.
The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years?
_____?
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
"I have this chart that talks about the half life of these and they are all different. I am not really understanding what the concept is here. How do I even attempt to answer this question...I don't even understand. I looked up half-life and it just doesn't make sense. Please explain and help me solve this problem.
The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years?
_____?"

Half-life is how long it takes for a particular element, in this case Radium-226 to decrease by half. If there is just one radioactive atom you will not end up with half an atom, there will be either 0 atoms left or one atom left. Different elements decay at different rates.

N sub t = quantity still remaining after time t
N sub 0 = initial quantity
t sub 1/2 = half-life of decaying element
N sub t = N sub 0 * (1/2)^(t / t sub 1/2)

N sub 0 = 100 mg
t sub 1/2 = 1590 years

let N sub t = 50 mg
50 = 100 * (1/2)^(t/1590)
50/100 = (1/2)^(t/1590)
1/2 = (1/2)^(t/1590)
t must be 1590 years

now for 3000 years:
N sub 0 = 100 mg
N sub t = ?
t = 3000 years
t sub 1/2 = 1590 years
N sub t = 100 * (1/2)^(3000/1590)
N sub t = 27.040759 mg to 6 places
N sub t = 27.041 mg to 3 places

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