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)