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Sagot :
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 ([tex]m(t)[/tex]), in grams, is described by the formula in time ([tex]t[/tex]), in minutes:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass of the isotope, in grams.
[tex]\tau[/tex] - Time constant, in minutes.
In addition, the time constant associated with the isotope decay can be described in terms of half-life ([tex]t_{1/2}[/tex]), in minutes:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (2)
If we know that [tex]m(t) = 7.5\,g[/tex], [tex]m_{o} = 120\,g[/tex] and [tex]t_{1/2} = 3.053\,min[/tex], then the time taken by the isotope is:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex]
[tex]\tau = \frac{3.053\,min}{\ln 2}[/tex]
[tex]\tau \approx 4.405\,min[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
[tex]t = -(4.405\,min)\cdot \ln \left(\frac{7.5\,g}{120\,g} \right)[/tex]
[tex]t \approx 12.213\,min[/tex]
12.213 minutes will be taken for 120 g-Thalium-208 to decay to 75 grams.
12.21 minutes will it take for 120 g of Thallium-208 to decay
to 7.5 g.
What is half life period?
Half life period is that time in which half of the reactant is convert into product.
In the question it is given that,
Initial mass of Thallium-208 = 120g
Final mass after decay = 7.5g
And half life of this decay = 3.053 min
Here we can calculate the total time of decay by the formula : T = t × n.
Where, T = total required time
t = half life
n = no. of half life required to decompose reactant.
120 → 60 →30 → 15 → 7.5
From the above sequence it is clear that we require 4 times of half life to decompose 120g to 7.5g.
So, T = 3.053 × 4 = 12.21 minutes
Hence, 12.21 minutes will it take to decay.
To learn more about half life, visit below link:
https://brainly.com/question/2320811
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