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.


Related Questions

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(check upload for chart)
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D.
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ANSWER FAST PLEASE!!
Which is a true statement about a zero net force?
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C.A zero net force causes a change to an object’s acceleration.
D.A zero net force causes no change in an objects motion.

Answers

Answer:

D)a zero net force causes no change in an objects motion.

A zero net force causes no change in an object's motion. This statement is true about zero net force. Therefore, option D is correct.

What is zero net force ?

An item that is originally at rest and has no net forces operating on it will stay at rest. If it is going, it will keep moving straight forward at a consistent speed. Forces are "pushes" or "pulls" on the object, and they are vector numbers, just like acceleration and velocity.

A automobile travelling at 50 mph on a highway continually has a net force of zero even though it is moving, since there is no acceleration and the speed is constant.

The total net force acting on an object as it moves at a steady speed is always zero. If you apply force, friction or another force (or several forces) will balance it out.

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Maria wants to determine which type of disinfectant kills the most bacteria.

Which of the following is the best way for Maria to determine this?
A.
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B.
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C.
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Answers

Answer:

Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied.

Explanation:

a coherent, typically large body of matter with no definite shape

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Answers

The answer to the question is A

Answer:

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Answers

Answer:

Sulpher

Explanation:

For this type of questions; calculate the total number of electrons so that you can identify the element from the periodic table.

Neon has 10 electrons. and from 3s^2 and 3p^4 there are 6 electrons.

So the total number of electrons is 16.

The element is Sulpher from group 6 of the periodic table

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Answers

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Answer:

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Explanation:

What type of mixture is separated by effusion and condensation?
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Answers

Answer:

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During a scientific investigation, which step will a scientist perform first?

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Answer:

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How long does it take for the water to start boiling? At what temperature does the water boil?

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Answer:

At sea level, or at zero feet in altitude, the boiling point of water is at 212 °F (100 °C). Once the water has reached this boiling point, the US Center for Disease Control recommends keeping it at a rolling boil for about a minute to make sure it is purified.

Answer:

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Explanation:

its true

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Answer:

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What is the pi of 80,000 and 400000

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Answer:

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thank u for being there for me when no one else was

btw she visited me last night "I made sure to punch her in da nose but my fist hit the wall instead of her face so yea funnn" good luck in this life

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Explanation:

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Answer:

liquid

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Answer:

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Which of the following best describes a function of the nervous system as
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Answer: The answer is to receive stimuli from inside and outside the body.

Explanation:

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Answers

Answer:

Axis

Anatomy

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In political science, a revolution is a fundamental and relatively sudden change in political power and political organization which occurs when the population revolts against the government, typically due to perceived oppression or political incompetence.

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:) gimme a crown plz

fghgfgfgfftftftft ttcc

Answers

Answer:

fghgfgfgftftftftftft ttcc

tehee

Explanation:

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Answers

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To solve this we must be knowing each and every concept related to nervous system. Therefore, "the muscular and skeletal system " is the correct option.

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The nervous system serves as a link between the environment and the organism's interactions. The nervous system coordinates actions or sensory information by sending and receiving signals to and from various sections of the body.

The peripheral and central systems are the two sections of the nervous system. They aid in the appropriate step-by-step coordination of the many physical reactions and communications from the parts of the body to the brain and back. The muscular and skeletal system, the nervous system work with to direct behavior and movement.

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Answers

Answer:

B

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Answers

Answer:

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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:

Yes it is

Explanation:

calcium chloride  releases heat in an exothermic reaction.

yes.

hope is helps! :)

The formula for density (D) is D = m/v, where m is mass and v is volume. What is the mass in grams (g) of a 45.0 cubic centimeters (cm³) block of silicon if the density of silicon is 2.336 grams per cubic centimeters (g/cm³)

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B. the mass is 19.3 g.
C. the mass is 45.0 g.
D. the mass is 105 g.

Answers

Answer:

The answer is D. The mass is 105g.

3.Zinc has an atomic number of 30 and a mass number of 65, how many neutrons does it have?
30
65
35
95

Answers

So your answer is 35 right okay so you subtract the mass number and the atomic number and that should always give you the neutrons

Answer:

35

Explanation:

Given parameters:

  Atomic number of zinc  = 30

  Mass number of zinc = 65

Unknown

  Number of neutrons  = ?

Solution:

The mass number of an atom is the sum of its protons and neutrons;

     Mass number  = Protons + neutrons

Atomic number is the number of protons in an atom;

   Atomic number  = Protons

So;

     Mass number  = Atomic number + Neutrons

Neutrons  = Mass number  - Atomic number

 Neutrons  = 65 - 30  = 35

The number of neutrons in the atom is 35

Which type of fault is under compression? A. Normal. B. Thrust. C. Transform. D. Strike-slip

Answers

Answer:

The answer is Thrust

If an atom has 3 protons, what is its atomic number?

Answers

Answer:

Atomic Number = 3.

Explanation:

The number of protons determines the atomic number. Basically the number of protons is the exact same as the atomic number.

Protons 3 = Atomic number 3

Apps
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Answers

Answer:

they are the three states of matter

3.
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88m square. Find
the dimensions.​

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

Total surface area of a cuboid =2(l×b+b×h+l×h)

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

2( x*2x + 2x*3x + x*3x )=88m

22x^2 =88

x=2

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

Pls fill in the blank

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A. Metalloids

B. Sodium

C. Gold

Answers

A. Metalloids

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3. How do you observe stuff?

Answers

Answer:

by looking at the and researching for super long

Explanation:

By reaching or looking
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