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? y = a * (.5) ^ (1/7)

Answer 1

Its actually 72.7

Explanation:

Answer 2

`t \approx 50.4\,min`

Explanation:

The time constant of the element X is:

`\tau = (13\,min)/(\ln 2)`

`\tau = 18.755\,min`

The decay function has the following form:

`(m)/(m_(o)) = e^{-(t)/(\tau) }`

`t = -\tau \cdot \ln (m)/(m_(o))`

`t = -(13\,min)\cdot \ln \left((11\,g)/(530\,g) \right)`

`t \approx 50.4\,min`