Suppose you found a material in which 12.5% of the original radioactive atoms were present. If the half-life is 10years, how old is the material?

Answers

Answer 1

Answer:

The material is 30 years old.

Explanation:

The decay of radioactive isotopes can be modelled by the following ordinary differential equation:

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

Where:

[tex]m(t)[/tex] - Current mass of the isotope, measured in grams.

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

[tex]\frac{dm}{dt}[/tex] - Rate of change of the isotope in time, measured in grams per year.

After some handling, we find that the solution of the differential equation is:

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

Where:

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

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

Now we clear time within the expression above:

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

Besides, we determine the time constant in terms of the half-life ([tex]t_{1/2}[/tex]), measured in years:

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

If we know that [tex]t_{1/2} = 10\,yr[/tex] and [tex]\frac{m(t)}{m_{o}} = 0.125[/tex], then the age of the material is:

[tex]\tau = \frac{10\,yr}{\ln 2}[/tex]

[tex]\tau = 14.427\,yr[/tex]

[tex]t = -(14.427\,yr)\cdot \ln 0.125[/tex]

[tex]t \approx 30\,yr[/tex]

The material is 30 years old.


Related Questions

8
Calcium carbonate (limestone) decomposes when heated.
Caco, + CaO + CO2

b) Calculate the volume of carbon dioxide produced if 10 grames were decomposed.​

Answers

Explanation:

Equation -

CaCO₃ → CaO + CO₂

molecular masses of -

CaCO₃ = 40+12+16×3 = 100 g/mol

CaO = 40+16 = 56 g/mol

CO₂ = 12+16×2 = 44 g/mol

Now,

If 100 g of CaCO₃ is decomposed then it produces 56 g of CaO and 44g of CO₂

Then,

If 1 g of CaCO₃ is decomposed then it produces 56/100g of CaO and 44/100g of CO₂

Now,

Here in question, 10g of CaCO₃ is decomposed

It means, It produces

56/100 × 10 = 56/10 = 5.6 g of CaO and

44/100 × 10 = 44/10 = 4.4 g of CO₂

Now,

we get that 10 g of CaCO₃ on burning produces 4.4 g of CO₂

we need to calculate volume of 4.4 g of CO₂

mole = mass/Gram molecular mass

Then,

mole = 4.4/44 = 0.1

Now,

volume = mole × 22.4 (in Litres)

= 0.1 × 22.4 = 2.24 L

Hence,

2.24 L of CO₂ will be produced when 10g of CaCO₃ decomposed.

In a chemical reaction, what happens to the total number of each type of atom?
A
The total number of each type of atom always stays the same.

B
The total number of each type of atom either increases or decreases.

C
The total number of each type of atom always increases.

D
The total number of each type of atom always decreases.

Answers

Answer:

A

Explanation:

The total number of each type of atom always stay the same.

How does a longshore current change the beach

Answers

Answer:

As this sheet of water moves on and off the beach, it can “capture” and transport beach sediment back out to sea. This process, known as “longshore drift,” can cause significant beach erosion.

Carbon dioxide is formed by the given formula.
C(s)+O2(g)→CO2(g)
Carbon dioxide is
A
a compound of two elements, carbon and oxygen.

B
a mixture of two compounds, carbon and oxygen.

C
a compound of two atoms, carbon and oxygen.

D
an element of two atoms, carbon and oxygen.

Answers

Answer:

A

Explanation:

Which of the following are electromagnetic waves? *

Water waves

Sound waves

Radio waves

Seismic waves

Answers

electromagnetic waves are radio waves.

First person to comment there crush name get brainlyest

Answers

Answer:

:0

Explanation:

David <3

As a result of the Law of Conservation of Mass, during a chemical change the mass of the
products are equal to the mass of the:
A. particles
B. elements
C. reactants
D. compounds

Answers

Answer:

D. Reactants.

Explanation:

The law of conservation of mass states that mass in an isolated system is neither created nor destroyed by chemical reactions or physical transformations. According to the law of conservation of mass, the mass of the products in a chemical reaction must equal the mass of the reactants.

....................D...........................

Who knows the answer to this please help

Answers

The number 4 try is because

Someone answer these please! It’s multiple choice

Answers

Answer: Number 1 is titanium.

The one where you calculate a tin block is 13.0cm.

3. Is A) Same Density And Same Chemical Properties.

4. Is also A. Ne

Explanation:

answer this pls thanks

Answers

Answer:  It is element nitrogen. It has an atomic number of 7 and the valence electron is 5. It needs 3 electrons to complete its octet state. That's why sometimes it has the oxidation number of -3 in ammonia.

Yeah i have no idea sorry

need help asap!!!!
will mark brainliest!!!

Answers

We can verify the properties as follows;

1) Sour taste - Put some soda on your tongue

2) Corrode metals - Put a little soda on a clean metal surface

3) Effect on Litmus paper - Dip a blue litmus paper in soda

4) Electrolysis - Add two electrodes to soda and connect a battery.

Does Soda show acidic properties?

Soda, specifically carbonated beverages like cola or soda pop, typically exhibits acidic properties. The acidity of soda is primarily due to the presence of carbonic acid (H₂CO₃), which forms when carbon dioxide gas (CO₂) dissolves in water.

When carbon dioxide is dissolved in water under high pressure, it forms carbonic acid through the following reaction:

CO₂ + H₂O ⇌ H₂CO₃

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What is an atomic nucleus

Answers

Answer:

The atomic nucleus is the small, dense region consisting of protons and net at the center of an atom.

Explanation:

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. ... Protons and neutrons are bound together to form a nucleus by the nuclear force.

Answer:

The atomic nucleus is the small , dense region consisting of protons and neutrons at the center of an atom .

scientists studying squirrels in a forest observed that the squirrel population decrease over a period of five years. which statement is the most likely explanation for the decrease in the population?​

Answers

Answer:

1.An increment of predators

2.unavailability of food resources due to change in climate causing famine

3.Spread of diseases over time that might kill the squirrels

4.An increment of squirrels which caused high competition on food,thus some of them had to migrate

5.Might be fire break out over some time that caused death to some squirrels in the reasoning of the period of time

Which of the following describes the energy transformations that occur when a toaster is used to make toast?

Thermal energy is transformed into chemical energy in the toaster, and chemical energy is transformed into thermal energy in the toast.

Electrical energy is transformed into thermal energy in the toaster, and chemical energy is transformed into thermal energy in the toast.

Light energy is transformed into thermal energy in the toaster, and thermal energy is transformed into chemical energy in the toast.

Electrical energy is transformed into thermal energy in the toaster, and thermal energy is transformed into chemical energy in the toast.

Answers

Answer:

Thermal energy (B)

Explanation:

just did it

Electrical energy is transformed into thermal energy in the toaster, and chemical energy is transformed into thermal energy in the toast. Hence option b is correct.

What is chemical energy?

Chemical energy is defined as chemical substances' potential energy, which is released as they experience chemical reactions and change into other substances. Additionally, it is what binds a substance's molecule's together. The body transforms or changes the chemical energy in food into heat and mechanical motion.

The wire attached to the power source transmits electrical energy to the toaster. The heating element is a part of the toaster. This heating element transforms electrical energy into heat energy, which aids in toast preparation, when it comes into contact with it. Thus, with an electric toaster, electrical energy is converted to heat energy.

Thus, electrical energy is transformed into thermal energy in the toaster, and chemical energy is transformed into thermal energy in the toast. Hence option b is correct.

To learn more about chemical energy, refer to the link below:

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Does the model correctly represent the electron dot diagram of magnesium? Why or why not? Check all that apply.
M g with 1 dot above and 1 right.
*{Yes, because the chemical symbol of magnesium is Mg.}
No, because the chemical symbol of magnesium is Mn.
*{Yes, because magnesium has two valence electrons.}
No, because magnesium has seven valence electrons.
No, because both of the dots should be on top of the chemical symbol

Answer 1 and 3

Answers

Answer:

1 and 3

Explanation:

Answer: A and B or 1 and 3

Explanation:

first to answer correctly gets brainleist! (you dont needa hear that vid thingy tahts just for ppl who cant read or need orial commidations or wtv lol)

Answers

I think the answer is c

Answer:

The seasons are a result of the tilt of the earth

What is the opposite force to pushing off the ground to jump?

Answers

Answer:

Newton's Third Law of Motion states that to every action there is an equal and opposite reaction. When the earth pushes on you to send you into the air after jumping, you also push on the earth with the same force. But forces are different from accelerations. A force F is a push or pull on an object

Explanation:

Answer:

Friction

Explanation:

Friction causes an opposite force

As water is cooled, its density increases until it reaches about
A. 4°C
B. 25°C
C. O'C
D. -2°C

Answers

About 4 C to for water density until it is cooled

whats the formula for mass

Answers

Answer:

The unit of molar mass is kg/mol. Where, m = mass, v = velocity.

Hope that helps :)

I NEED HELP!!
In a stream, how are particles such as silt, clay, and sand carried?
A. as dissolve load
B. as bed load
C. in suspension
D. in solution

In a stream, how are particles such as silt, clay, and sand carried?
A. particles rubbing together
B. An increase is suspended materials
C. an increase in the dissolve load
D. changes in the stream 's carrying capacity

The path of a stream can vary considerably, depending on the slope of the land and the
A. bedload of the stream
B. amount of rainfall
C. amount of hummus present in the soil
D. Type of material through which the stream flows

The amount of dissolved material that stream water carries is usually expressed in
A. cubic meters per second
B. parts per million
C. cubic feet per minute
D. grams per 1000 gallons

The carrying capacity of a stream depends on both the velocity and the
A. Temperature of the water
B. amount of water in the stream
C. type of material through which the stream flows
D. minerals dissolved in the stream

Answers

Answer:

1 B

2A

#D

3B

1D

2B

3C

4A

A,C,A,B

C,A,C,A

C,A,A,B

Explanation:

Easy ive done this brings back memories

In  ecosystem, particles are carried as  bed load by rubbing particles together.Path of stream can be varied depending on amount of humus present in  soil and is measured in cubic meters per second and carrying capacity depends on  type of material through which stream flows.

What is an ecosystem?

Ecosystem is defined as a system which consists of all living organisms and the physical components with which the living beings interact. The abiotic and biotic components are linked to each other through nutrient cycles and flow of energy.

Energy enters the system through the process of photosynthesis .Animals play an important role in transfer of energy as they feed on each other.As a result of this transfer of matter and energy takes place through the system .Living organisms also influence the quantity of biomass present.By decomposition of dead plants and animals by microbes nutrients are released back in to the soil.

Learn more about ecosystem,here:

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Can somebody help me with this??!

Answers

What is the question? What is it asking u to do

. The model shows Earth in several positions relative to the Sun. In which position is it winter in North America?​

Answers

What does the model look like
all the way to the right

Can someone tell me about kinetic, potential, and gravitational energy?

Answers

Answer:

the internet can teach you alot about all 3 things

Explanation:

Answer:

if you go on YT and search  kinetic, potential, and gravitational energy their will be a bill nye vid that is very informational on the topic at hand!!!

Explanation:

hope this helps!!

In order to change a solid to a liquid or a liquid to a gas, what is needed?
A high boiling point
An increase in thermal energy
A high melting point
A decrease in thermal energy
Hide hint for Question 9

Answers

answer: increase in thermal heat

explanation: In order to change the state, more energy is needed.
When you want to go from a lower state (solid) to a higher state (liquid) then you need more energy. and more energy means more heat in this case. if it was going from liquid to solid, you would need less thermal energy.

why do the Noble gases have the highest ionization energies across a period?

Answers

Answer:

ionization energy decreases from top to bottom in groups, and increases from left to right across a period. So technically, the noble games have the largest ionization energy.

Explanation:

Which of these describes a challenge that the engineer of a high-altitude
airplane would need to consider?
A. More fuel is used at higher altitudes.
B. The airplane may succumb to the power of gravity as lift
decreases at higher altitudes.
C. The airplane may need a heat shield for protection from sonic
booms.
O D. The airplane will create more drag at higher altitudes than lower
altitudes.

Answers

Answer:

I think its (B)

Explanation:

as when the air thins out at higher elevations, your lift decreases so at some point, the plane cant produce enough lift to overcome gravity.

The answer is option B.

What do radio waves and microwaves have in common?


Both are at the side of the spectrum that has the lowest frequency.


Both are found next to visible light on the electromagnetic spectrum.


Both are at the side of the spectrum that has the highest radiant energy.


Both are at the side of the spectrum that has the shortest wavelengths.

Answers

Answer:

Both are at the side of the spectrum that has the lowest frequency.

Explanation:

i took the test

Answer:

a

Explanation:

What makes the element oxygen different from the element hydrogen?

Answers

Answer: the difference is due to the fact that one water molecule has two hydrogen atoms to one oxygen this means it takes two water molecules (2 H2O) to make one oxygen molecule (02) .At the same time however two molecules of water (2 H20) can make two molecules of hydrogen (2 H20)

 

Explanation: hope this helped and mark me as brainliest please =)

Why are the Galápagos Islands such a place of interest to the world

Answers

Answer:

Explanation:

Use the equation below to solve the problem that follows.

2H2 (g) + O2 (g) → 2H2O (g)

When David reacts 13.8 grams of hydrogen gas with excess oxygen, 87.0 grams of water are formed. Calculate his percent yield of water.

Im very loss with this question

Answers

Percent yield of water : 70%

Further explanation

Reaction

2H₂ (g) + O₂ (g) → 2H₂O (g)

mol H₂(MW= 2 g/mol) :

[tex]\tt \dfrac{13.8~g}{2~g/mol}=6.9~mol[/tex]

mol H₂O = mol H₂ = 6.9

mass H₂O(theoretical) :

[tex]\tt 6.9\times 18~g/mol=124.2~g[/tex]

[tex]\tt \%yield=\dfrac{actual}{theoretical}\times 100\%\\\\\%yield=\dfrac{87}{124.2}\times 100\%=70\%[/tex]

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