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

Answer:

$t \approx 50.4\,min$

Step-by-step explanation:

The time constant of the element X is:

$\tau = \frac{13\,min}{\ln 2}$

$\tau = 18.755\,min$

The decay function has the following form:

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

$t = -\tau \cdot \ln \frac{m}{m_{o}}$

$t = -(13\,min)\cdot \ln \left(\frac{11\,g}{530\,g} \right)$

$t \approx 50.4\,min$