Example

If Radium has a half life of 1620 yrs, how long will it take to decay to 20% of its original radioactivity?

t_½  = 1620

[A]₀  = 100%

[A]  = 20%

To find t we need to know k, therefore we use equation (2) first;

kt_½ = ln2

k = 0.693/1620    = 4.28 x 10^{^-4}

We can now use equation (1) to find t;

kt = ln{[A]₀/[A]}

kt = ln(100/20)    = 1.609

t = 1.609/4.28 x 10^{^-4}   = 3760.4 yrs

Try it yourself!

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