Question

Element X decays radioactively with a half life of 13 minutes. If there are 530 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 11 grams?

Answer 1

72.7 minutes

Explanation:

From the above question, we can deduce that we are to find the time(t) of decay.

The formula used for this calculation is given as:

N(t) = No(1/2)^t/t½

N(t) = quantity of the substance remaining = 11 grams

No = initial quantity of the substance = 530 grams

t = time elapsed

t½ = half life of the substance = 13 minutes

Making t , the subject of the formula

t = t½ × In(N(t)/No)/-In2

t = 13 × In(11/530)/-In2

t = 72.675420100572minutes

Approximately 72.7 minutes