Radioactive isotope X has a half-life of 500,000 years. This isotope may be found in some types of volcanic rocks. A particular sample of volcanic rock taken from a layer that covered up some of the earliest known human-like footprints contains 0.125 mg of isotope X. The volcanic rock sample originally contained 8.00 mg of isotope X. How long ago were these footprints made. I need the equation. Thanks. please I am stuck on this question. PLEASE

Answers

Answer 1

Answer:

The age of the earliest known human-like footprints is approximately 3000000 years.

Explanation:

Decay of isotopes is represented by the following ordinary differential equation:

[tex]\frac{dm}{dt} = -\frac{m}{\tau}[/tex] (Eq. 1)

Where:

[tex]\frac{dm}{dt}[/tex] - First derivative of mass with respect to time, measured in miligrams per year.

[tex]m[/tex] - Current mass of the isotope, measured in miligrams.

[tex]\tau[/tex] - Time constant, measured in years.

Now we proceed to obtain the solution of the differential equation:

[tex]\int\limits {\frac{dm}{m} } = -\frac{1}{\tau}\int dt[/tex]

[tex]\ln m = -\frac{t}{\tau}+C[/tex]

[tex]m(t) = e^{-\frac{t}{\tau}+C }[/tex]

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (Eq. 2)

Where:

[tex]m_{o}[/tex] - Initial mass of the isotope, measured in miligrams.

[tex]t[/tex] - Time, measured in years.

[tex]\tau[/tex] - Time constant, measured in years.

We proceed to clear time within the formula presented above:

[tex]\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}[/tex]

[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]

In addition, time constant can be found as a function of half-life:

[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (Eq. 3)

If we know that [tex]t_{1/2} = 500000\,yr[/tex], [tex]m_{o} = 8\,mg[/tex] and [tex]m(t) = 0.125\,mg[/tex], the age of the earliest known human-like footprints is:

[tex]\tau = \frac{500000\,yr}{\ln 2}[/tex]

[tex]\tau \approx 721347.520\,yr[/tex]

[tex]t = -(721347.520\,yr)\cdot \ln \left(\frac{0.125\,mg}{8\,mg} \right)[/tex]

[tex]t \approx 3000000\,yr[/tex]

The age of the earliest known human-like footprints is approximately 3000000 years.


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Answers

Answer:

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Answer:

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Answers

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Unknown

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There are equally valid arguments for placing hydrogen in Group VIIA. It forms compounds (such as NaH and CaH2) that are analogs of halogen compounds (such as NaF and CaCl2). It also combines with other nonmetals to form covalent compounds (such as H2O, CH4, and NH3), the way a nonmetal should. Finally, the element is a gas at room temperature and atmospheric pressure, like other nonmetals (such as O2 and N2).

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Answers

Answer:

The length of the cuboid =x=2m, breadth =2x=4m, height =3x=6m

Explanation:

Let the length of the cuboid =x, breadth =2x, height =3x

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Given, total surface area of the cuboid =88m^2

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Hence, the length of the cuboid =x=2m, breadth =2x=4m, height =3x=6m

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