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

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)

A. the mass is 0.0519 g.
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.

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

A worker is melting samples of various metals. Which sample will require the most heating to melt?
(check upload for chart)
A.
1 kg of aluminum
B.
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C.
3 kg of silver
D.
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3kg of silver is the answer

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

What type of mixture is separated by effusion and condensation?
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c.
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b.
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d.
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Answers

Answer:

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3.
The dimensions of a cuboid are in the ratio of 1:2:3 and its total surface area is
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

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

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

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

Answers

Answer:

The answer is Thrust

HELP MEEEEEEEEEEEE
Winds and ocean breezes occur due to _____________.

A. None of these
B. Conduction currents
C. Boiling
D. Convection currents

Answers

Answer:

B

Explanation:

it flows by the conduction currents

Quartzite is a coarse-grained rock derived from sandstone.

Which type of rock is quartzite?


metamorphic


extrusive


sedimentary


igneous

Answers

its a metamorphic rock

Answer:

granoblastic metamorphic rock

Explanation:

[Ne] 3s^ 2 3p^ 4 can someone tell me the element

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

Can yall plz help me!!!!!!!!!!!!

Define the terms below:
● Axis:
● Rotation:
● Revolution:
● Elliptical Orbit:

Answers

Answer:

Axis

Anatomy

In anatomy, the second cervical vertebra of the spine is named the axis or epistropheus. By the atlanto-axial joint, it forms the pivot upon which the first cervical vertebra, which carries the head, rotates.

Rotation

A rotation is a circular movement of an object around a center of rotation. A three-dimensional object can always be rotated about an infinite number of imaginary lines called rotation axis. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin.

Revolution

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.

Elliptic orbit

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.

:) gimme a crown plz

Hydrogen is in column 1 of the periodic table. What information does this give us? (2 points)

There is one other element that hydrogen will bond with.

There is one neutron in the nucleus.

The mass of the atom is one.

There is one electron in the outer energy level.

Answers

Answer:

the last one

Explanation:

ydyeusueueueueudhs

Because hydrogen forms compounds with oxidation numbers of both +1 and -1, many periodic tables include this element in both Group IA (with Li, Na, K, Rb, Cs, and Fr) and Group VIIA (with F, Cl, Br, I, and At).

There are many reasons for including hydrogen among the elements in Group IA. It forms compounds (such as HCl and HNO3) that are analogs of alkali metal compounds (such as NaCl and KNO3). Under conditions of very high pressure, it has the properties of a metal. (It has been argued, for example, that any hydrogen present at the center of the planet Jupiter is likely to be a metallic solid.) Finally, hydrogen combines with a handful of metals, such as scandium, titanium, chromium, nickel, or palladium, to form materials that behave as if they were alloys of two metals.

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).

It is difficult to decide where hydrogen belongs in the periodic table because of the physical properties of the element. The first ionization energy of hydrogen (1312 kJ/mol), for example, is roughly halfway between the elements with the largest (2372 kJ/mol) and smallest (376 kJ/mol) ionization energies. Hydrogen also has an electronegativity (EN = 2.20) halfway between the extremes of the most electronegative (EN = 3.98) and least electronegative (EN = 0.7) elements. On the basis of electronegativity, it is tempting to classify hydrogen as a semimeta

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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

If anyone have the answers to this plz tell me

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Explanation:

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

fghgfgfgfftftftft ttcc

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Answer:

fghgfgfgftftftftftft ttcc

tehee

Explanation:

Which of the following best describes a function of the nervous system as
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to store urine
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to receive stimuli from inside and outside the body
to take in oxygen and transport it to the cells

Answers

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

Explanation:

Is calcium chloride reactive?

Answers

Answer:

Yes it is

Explanation:

calcium chloride  releases heat in an exothermic reaction.

yes.

hope is helps! :)

A sample of matter is made up of three different atoms that are chemically combined. What
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Answers

Answer:

liquid

Explanation:

a molecule consists of different atoms chemically combined. A molecule is also a liquid. Molecules make up ice cubes, which are also small water particles which arr yet again liquid.

ANSWER FAST PLEASE!!
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B.zero net force causes a change to an object’s speed.
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.

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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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A. Metalloids

B. Sodium

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Answers

A. Metalloids

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The muscular and skeletal system because we use our brain to move our body it sends a signal to move that muscle that we want to use

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.

What is nervous system?

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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Where are hormones produced in animals, and how are they transported throughout the body?
A. Animal hormones are produced in endocrine glands and travel through the blood.
B. Animal hormones are produced in lymph nodes and travel through the lymphatic system.
C. Animal hormones are produced inside the bones and travel through the nervous system.
D. Animal hormones are produced in sweat glands and travel through the skin.

Answers

Answer:

Vertebrate Endocrine Glands and Hormones

Unlike plant hormones, animal hormones are often (though not always) produced in specialized hormone-synthesizing glands (shown below). The hormones are then secreted from the glands into the blood stream, where they are transported throughout the body.

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Answers

Answer:

by looking at the and researching for super long

Explanation:

By reaching or looking

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.
Interview ten different people to determine which type of disinfectant they prefer.
B.
Put the same amount and species of bacteria on ten identical plates, and add ten different kinds of disinfectant to each plate.
C.
Ask ten different companies that make disinfectants which type is best.
D.
Put the same amount and species of bacteria on ten identical plates, and add a different disinfectant to each plate.

Answers

A I think thats what I would put

N= 0.785 mol N2
P= 1.5 atm
T= 301 K
V=?
FAST PLZ ​

Answers

Answer:

V=13.031L

Explanation:

Use the equation PV=nRT. n is moles, R is 8.31, T is temp in (K), and Pressure in KPa

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

Answers

Answer:

you need to have a question or a problem first

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

Apps
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Answers

Answer:

they are the three states of matter

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a. the number of offspring
b. genetic variation
c. genetic mutations​

Answers

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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