Need help understanding HSC question (1 Viewer)

BlueGas · Jul 10, 2015

I'm having trouble with 2014 HSC question 13 b. ii)

What I dont get is if the half life of the material is 300 years, doesn't that mean it takes 600 years for the material to completely decay? How could you figure out what is remaining after 1000 years?

InteGrand · Jul 10, 2015

BlueGas said:
I'm having trouble with 2014 HSC question 13 b. ii)

What I dont get is if the half life of the material is 300 years, doesn't that mean it takes 600 years for the material to completely decay? How could you figure out what is remaining after 1000 years?

$No, it refers to the time taken for half of the currently remaining amount to decay at any given time. This is exponential decay, so technically it never decays completely (it asymptotically approaches this).$

$Exponential decay with half-life $\tau$ is of the form $A(t) = A_0 \times 2^{-\frac{t}{\tau}}$, where $A(t)$ is the amount present at time $t\geq 0$ and $A_0$ is initial amount. Use the given info to deduce the value of $A_0$, then substitute the required time to find the amount present at that time.$

Ambility · Jul 10, 2015

A half life if the time it takes for half of a substance to decay. If the half life is 300 years, after 300 years, there will be half the material. However, if you wait another 300 years, you will have half of what you had after 300 years. So in 600 years you have 1/4 the material remaining. In 900 years you have 1/8 the material remaining and so forth...

BlueGas · Jul 10, 2015

Thanks lads!

Need help understanding HSC question (1 Viewer)

BlueGas

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InteGrand

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Ambility

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BlueGas

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