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Grace [21]
2 years ago
5

Element X decays radioactively with a half life of 13 minutes. If there are 530 grams of Element X, how long, to the nearest ten

th of a minute, would it take the element to decay to 11 grams? y = a * (.5) ^ (1/7)
Mathematics
1 answer:
Leona [35]2 years ago
6 0

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

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Given:

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