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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Answer:

you need to have a question or a problem first

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C. Gold

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A. Metalloids

They can either lose an electron or share an electron when it combines with other elements. They have some properties of metals and some properties of non-metals.

What is the pi of 80,000 and 400000

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Answer:

london I'm not dead -yet-

Explanation:

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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Answers

Answer:

V=13.031L

Explanation:

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Which of the following best describes a function of the nervous system as
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to store urine
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Answers

Answer: The answer is to receive stimuli from inside and outside the body.

Explanation:

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

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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

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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.

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So the total number of electrons is 16.

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3kg of silver is the answer

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The answer to the question is A

Answer:

a. the number of offspring would be ur answer pls make me brainliest

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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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Answer:

The answer is Thrust

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Which is a true statement about a zero net force?
A zero net force causes a change to an object’s direction.
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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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Answers

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:

Water boils at 212 degrees fahrenheit or 100 degree celcius

Explanation:

its true

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Answers

Answer:

B

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Answers

Answer:

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Answers

Answer:

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Explanation:

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

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Answers

Answer:

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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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In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1.

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Answers

Answer:

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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.

Therefore, "the muscular and skeletal system " is the correct option.

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Answers

Explanation:

hey can I please get the passage so that I can help you

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

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A.
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A I think thats what I would put

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Answers

Answer:

by looking at the and researching for super long

Explanation:

By reaching or looking

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Answers

Answer:

Vertebrate Endocrine Glands and Hormones

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Apps
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Answer:

they are the three states of matter

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Answers

Answer:

Yes it is

Explanation:

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yes.

hope is helps! :)

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Answers

its a metamorphic rock

Answer:

granoblastic metamorphic rock

Explanation:

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Answers

Answer:

c is the answer then check it out

fghgfgfgfftftftft ttcc

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Answer:

fghgfgfgftftftftftft ttcc

tehee

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