Element X decays radioactively with a half life of 14 minutes. If there are 760 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 11 grams?

85.5 minutes

Step-by-step explanation:

The amount of an element that will remain after time t can be expressed as a function of initial amount N0, time t, and half life th as;

Nt = N0 * e^ (-λt)

Where;

Decay constant λ = ln (2) / th, substituting into the equation;

Nt = N0 * e^ (-ln (2) t/th)

We need to make t the subject of formula;

Nt/N0 = e^ (-ln (2) t/th)

ln (Nt/N0) = - ln (2) t/th

t = ln (Nt/N0) : - ln (2) / th

Given;

Initial amount N0 = 760g

Final amount Nt = 11 g

Half life th = 14 minutes

the nearest tenth of a minute, would it take the element to decay to 11 grams can be derived using the formula;

t = ln (Nt/N0) : - ln (2) / th

Substituting the given values;

t = ln (11/760) : - ln (2) / 14

t = 85.5 minutes