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kozerog [31]
2 years ago
7

9. Thallium-208 has a half-life of 3.053 min. How long will it take for 120 g of it to decay

Chemistry
1 answer:
damaskus [11]2 years ago
4 0

Answer:

12.213 minutes will be taken for 120 g-Thalium-208 to decay to 75 grams.

Explanation:

Radioactive isotopes decay exponentially in time, the mass of the isotope (m(t)), in grams, is described by the formula in time (t), in minutes:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} } (1)

Where:

m_{o} - Initial mass of the isotope, in grams.

\tau - Time constant, in minutes.

In addition, the time constant associated with the isotope decay can be described in terms of half-life (t_{1/2}), in minutes:

\tau = \frac{t_{1/2}}{\ln 2} (2)

If we know that m(t) = 7.5\,g, m_{o} = 120\,g and t_{1/2} = 3.053\,min, then the time taken by the isotope is:

\tau = \frac{t_{1/2}}{\ln 2}

\tau = \frac{3.053\,min}{\ln 2}

\tau \approx 4.405\,min

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

t = -(4.405\,min)\cdot \ln \left(\frac{7.5\,g}{120\,g} \right)

t \approx 12.213\,min

12.213 minutes will be taken for 120 g-Thalium-208 to decay to 75 grams.

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