The half-life of Strontium-90 is 28 a. If 60 g of this isotope is currently in a sample of soil, estimate the amount in the same sample 84 a later.
So I did a=60g(1/2)^84/28
But I don't know if thats correct.
Thank for your help!
Ok, that will do it, but natural logs are better...
amount=60 e^(-.693*84/28)
To determine the amount of Strontium-90 in the sample 84 years later, you can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the amount of the isotope at time t
N₀ is the initial amount of the isotope
t is the time that has passed
h is the half-life of the isotope
In this case, N₀ = 60g, t = 84 years, and h = 28 years.
Plugging in the values, the equation becomes:
N(84) = 60g * (1/2)^(84/28)
Simplifying:
N(84) = 60g * (1/2)^(3)
N(84) = 60g * (1/8)
N(84) = 7.5g
Therefore, based on the given information, the estimated amount of Strontium-90 in the sample 84 years later is 7.5 grams.
To estimate the amount of Strontium-90 remaining in the sample after 84 years, you are correct in using the half-life formula. The formula is:
N(t) = N₀(1/2)^(t/t₁/₂)
Where:
N(t) = amount of the isotope at time t
N₀ = initial amount of the isotope
t = time elapsed
t₁/₂ = half-life of the isotope
In this case, N₀ is given as 60 g, t is 84 years, and the half-life (t₁/₂) of Strontium-90 is 28 years. We can substitute these values into the formula:
N(84) = 60g * (1/2)^(84/28)
Now we can calculate this expression:
N(84) = 60g * (1/2)^(3) [since 84/28 = 3]
N(84) = 60g * (1/8)
N(84) = 7.5g
Therefore, the estimated amount of Strontium-90 remaining in the sample after 84 years is 7.5 grams.