1. ## Half Life

The half life of plutonium-239 is 24,360 years. The maximum amount an adult human can handle without injury is .13 micrograms (.000000013 grams). suppose a researcher possesses a 1-gram sample of plutonium - 239. the amount "A" (in grams) after "t" years is A(t) = 1 x (1/2)^ t/360

a) How much of 1-gram sample will remain after 10,000 years?

b) How long will it take before there is .000000013 grams left?

My issue is this: For part "A", how do I input 1/2 to the 10000/36th power on my calculator. I Have a TI-30Xa, yet I have been unable to figure out how to enter this formula.

For part B, is it as simple as counting the number of half lives that pass until I get an amount less than .13 micrograms?

2. I dont understand the formula for A(t).
shouldnt it be : A(t)=1 x (1/2)^(t/24360) as the half life is 24360 years, which mean, only after this time the quantity will be half it was

so the answer would be : A(10000)= (1/2)^(2,436) which is easier to calculate

anyway...did u find the solution for this?

3. Originally Posted by Hapa
The half life of plutonium-239 is 24,360 years. The maximum amount an adult human can handle without injury is .13 micrograms (.000000013 grams). suppose a researcher possesses a 1-gram sample of plutonium - 239. the amount "A" (in grams) after "t" years is A(t) = 1 x (1/2)^ t/360

a) How much of 1-gram sample will remain after 10,000 years?

b) How long will it take before there is .000000013 grams left?

My issue is this: For part "A", how do I input 1/2 to the 10000/36th power on my calculator. I Have a TI-30Xa, yet I have been unable to figure out how to enter this formula.

For part B, is it as simple as counting the number of half lives that pass until I get an amount less than .13 micrograms?

your equation is incorrect. it should be ...

$
A(t) = \left(\frac{1}{2}\right)^{\frac{t}{24360}}
$

now find A(10000)

$.13$ micrograms = $1.3 \times 10^{-7}$ grams

solve the equation for t using logs ...

$
1.3 \times 10^{-7} = \left(\frac{1}{2}\right)^{\frac{t}{24360}}
$