Question

q(t)= Q_0 e^-kt where Q represents the quantity remaining after t years and k is the decay constant 0.00043. How long will it take for 500g of radium to decay to 5g?

Answer 1

It takes 16,064 years for the 500g of radium to decay to 5g.

How long will it take for 500g of radium to decay to 5g?

Here we have the decay equation:

$Q(t) = Q_0*e^{-k*t}$

Where Q₀ is the initial amount, and k is the decay constant.

We know that:

Q₀ = 500g

k = 0.00043

And we want to find the value of t such that Q(t) = 5g, so we need to solve:

$5 = 500*e^{-0.00043*t}\\\\5/500 = e^{-0.00043*t}\\\\0.001 = e^{-0.00043*t}$

Now we can apply the natural logarithm in both sides:

$ln(0.001) = ln(e^{-0.00043*t})\\\\ln(0.001) = -0.00043*t\\\\\frac{ln(0.001)}{-0.00043} = t = 16,064.5$

So it takes 16,064 years for the 500g of radium to decay to 5g.

If you want to learn more about decays:

https://brainly.com/question/7920039

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