Element X decays radioactively with a half life of 12 minutes. If there are 510 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 11 grams?

t = 66.4 minutes ( to the nearest tenth of a minute)

it would take the element 66.4 minutes to decay to 11 grams

Step-by-step explanation:

Given;

Initial amount N = 510 g

Final amount Nt = 11 g

Half life t(1/2) = 12 minutes

The amount of time t required for the Element X to decay from N to Nt can be written as;

t = ln(Nt/N) ÷ -λ 1

Where;

λ = decay constant

λ = ln(2)/t(1/2)

Substituting λ, equation 1 then becomes;

t = ln(Nt/N) ÷ -(ln(2)/t(1/2))

Substituting the values;

t = ln(11/510) ÷ -(ln(2)/12)

t = −3.8365 ÷ -0.05776

t = 66.419

t = 66.4 minutes ( to the nearest tenth of a minute)

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