how many molecules are there in 9.34 grams of water

Answers

Answer 1

Answer: [tex]3.13\times 10^{23}molecules[/tex]

Explanation: To calculate the moles, we use the formula:

[tex]Moles=\frac{\text{Given mass}}{\text{Molar mass}}=\frac{9.34g}{18g/mol}=0.52mol[/tex]  

1 mole of water contains=[tex]6.023\times 10^{23}molecules[/tex] of water

0.52 moles of water contain=[tex]\frac{6.023\times 10^{23}}{1}\times 0.52=3.13\times 10^{23}molecules[/tex] of water

Answer 2

One or more than one atoms bonds and makes up the molecules, it can be the same or different atoms that make up the compounds. Molecules present in the 9.34 gm of water are [tex]\rm 3.13 \times 10^{23}[/tex].

What is the formula for calculating molecules?

Given,

Mass of the water (m) = 9.34 gm

The molar mass of the water (M)= 18 g/mol

From the mass and the molar mass number of the moles can be estimated:

[tex]\rm Moles (n) = \dfrac{\;\rm Mass}{\rm Molar \;mass}[/tex]

Substituting values in the above formula:

[tex]\begin{aligned}\rm n &= \dfrac{9.34\;\rm g}{18\;\rm g/mol}\\\\&= 0.52\;\rm mol\end{aligned}[/tex]

We know that,

1 mole of water = [tex]\rm 6.023 \times 10^{23}[/tex] molecules of water

0.52 moles of water = X molecules

Solving for X:

[tex]\begin{aligned} \rm X &= 0.52 \times \rm 6.023 \times 10^{23}\\\\&= \rm 3.13 \times 10^{23}\end{aligned}[/tex]

Therefore, [tex]\rm 3.13 \times 10^{23}[/tex] molecules are present.

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Related Questions

The wavelength of light in the infrared region is 4.257 × 10-7 cm. What is the frequency of this light?

Answers

7.04×10^14 is the frequencyof light by the relation:
wavelength= wave velocity/frequency

Find the half-life of an element which decays by 3.415% each day.

Answers

Final answer:

The half-life of an element that decays by 3.415% each day is approximately 20.27 days.

Explanation:

The half-life of an element can be calculated using the formula:

half-life = (ln(2)) / (decay constant)

where the decay constant is the rate at which the element decays per time period. In this case, the element decays by 3.415% each day. To find the decay constant, we convert the percentage to a decimal by dividing it by 100:

decay constant = 0.03415

Now we can calculate the half-life:

half-life = (ln(2)) / (0.03415)

A calculator can be used to find the value of ln(2), which is approximately 0.693:

half-life = 0.693 / 0.03415 = 20.27 days

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What mass of KBr (in grams) should you use to make 150.0 mL of a 1.70 M solution of KBr?

Answers

V = 150.0 mL = 0.15 L
c = 1.70 M
m=?
For the purpose, the equation for molar concentration is necessary:
c=n/V
From the equation we can determine the number of moles:
n= cxV = 1.70M x 0.15L = 0.255 mole
Now we can calculate the mass:
m = nxM = 0.255 x 119= 30.34 g is necessary 


Final answer:

To make 150.0 mL of a 1.70 M KBr solution, you need 30.33 grams of KBr. This is calculated by multiplying the molarity (1.70 M), the volume in liters (0.150 L), and the molar mass of KBr (119.00 g/mol).

Explanation:

To calculate the mass of KBr needed to make 150.0 mL of a 1.70 M solution, we need to use the formula:

Mass (g) = Molarity (M) × Volume (L) × Molar Mass (g/mol)

First, convert the volume from milliliters to liters by dividing by 1000:

150.0 mL = 0.150 L

Next, find the molar mass of KBr, which is the sum of the atomic masses of potassium (K) and bromine (Br). Potassium has an atomic mass of 39.10 g/mol, and bromine has an atomic mass of 79.90 g/mol:

Molar Mass of KBr = 39.10 g/mol + 79.90 g/mol = 119.00 g/mol

Now, we can calculate the mass of KBr:

Mass of KBr = 1.70 M × 0.150 L × 119.00 g/mol = 30.33 grams

Therefore, you should use 30.33 grams of KBr to make the solution.

What is the equilibrium associated with ka3 for h3po4?

Answers

Phosphoric acid has 3 pKa values (pKa1=2.1,  pKa2=6.9, pKa3= 12.4) and after 3 ionization it gives 3 types of ions at different pKa values: 

H₃PO₄(aq) + H₂O(l) ⇌ H₃O⁺(aq) + H₂PO₄⁻ (aq)         pKₐ₁ 


H₂PO₄⁻(aq) + H₂O(l) ⇌ H₃O⁺(aq) + HPO₄²⁻ (aq)       pKₐ₂


HPO₄²⁻(aq) + H₂O(l) ⇌ H₃O⁺(aq) + PO₄³⁻ (aq)          pKₐ₃ 

The last equilibrium is associated with the highest pKa value (12.4) of phosphoric acid. There the last OH group will lose its hydrogen and hydrogen phosphate ion (HPO₄²⁻) turns into phosphate ion (PO₄³⁻).

The equilibrium associated with [tex]\text{K}_{a3}[/tex] for [tex]\text{H}_3\text{PO}_4[/tex] is as follows:

 [tex]\boxed{\text{HPO}^{2-}_{4}(aq)+\text{H}_{2}\text{O}(l)_{\rightleftharpoons}^{{K}_{a3}}\text{PO}^{3-}_{4}(aq)+\text{H}_{3}\text{O}^{+}(aq)}[/tex]

Further Explanation:

Acids are substances that can donate hydrogen ion [tex]\text{H}^{+}[/tex] or proton in their aqueous solutions.

Classification of acids:

1. Monoprotic acids

Acids that are capable to donate single proton in solutions are monoprotic acids. For example, HCl is a monoprotic acid due to its tendency to donate only one proton in solutions.

2. Polyprotic acids

Acids that are capable to donate more than one proton in aqueous solutions are called polyprotic acids. For example, [tex]\text{H}_2\text{SO}_4[/tex] and [tex]\text{H}_3\text{PO}_4[/tex] are all polyprotic acids.

Acid strength is measured with the help of dissociation constant. Itis denoted by [tex]\text{K}_a[/tex]. Since [tex]\text{H}_3\text{PO}_4[/tex] contains three hydrogens in it, it can donate three hydrogen ions in solutions so it is triprotic acid.

Dissociation of [tex]\text{H}_3\text{PO}_4[/tex] occurs as follows:

[tex]\begin{aligned}\text{H}_3\text{PO}_4(aq)+\text{H}_2\text{O}(l)_{\rightleftharpoons}^{K_{a1}}\text{H}_2\text{PO}^{-}_{4}(aq)+\text{H}_3\text{O}^{+}(aq)\\\text{H}_2\text{PO}^{-}_{4}(aq)\text{H}_2\text{O}(l)_{\rightleftharpoons}^{K_{a3}}\text{HPO}^{2-}_{4}(aq)+\text{H}_{3}\text{O}^{+}(aq)\\\text{HPO}^{2-}_{4}(aq)+\text{H}_{2}\text{O}(l)_{\rightleftharpoons}^{K_{a3}}\text{PO}^{3-}_{4}(aq)+\text{H}_{3}\text{O}^{+}(aq)\end{aligned}[/tex]  

Where,

[tex]{{\text{k}}_{{\text{a1}}}}[/tex] is the first dissociation constant of [tex]{{\text{H}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}[/tex].

[tex]{{\text{k}}_{{\text{a2}}}}[/tex] is the second dissociation constant of [tex]{{\text{H}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}[/tex].

[tex]{{\text{k}}_{{\text{a3}}}}[/tex] is the third dissociation constant of [tex]{{\text{H}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}[/tex].

The expression of [tex]{{\text{k}}_{{\text{a3}}}}[/tex] for [tex]{{\text{H}}_{\text{3}}}{\text{P}}{{\text{O}}_{\text{4}}}[/tex] is as follows:

[tex]{{\text{k}}_{{\text{a3}}}} = \dfrac{{\left[ {{\text{PO}}_4^{3 - }} \right]\left[ {{{\text{H}}_{\text{3}}}{{\text{O}}^ + }} \right]}}{{\left[ {{\text{HPO}}_4^{2 - }} \right]}}[/tex]  

Learn more:

Calculation of equilibrium constant of pure water at 25°C: https://brainly.com/question/3467841 Complete equation for the dissociation of [tex]{\text{N}}{{\text{a}}_{\text{2}}}{\text{C}}{{\text{O}}_{\text{3}}}[/tex] (aq): https://brainly.com/question/5425813

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Equilibrium

Keywords: acids, monoprotic acid, polyprotic acid, hydrogen ions, ka3, H3PO4, acid strength, dissociation constant, first dissociation constant, second dissociation constant, third dissociation constant.

Which statement about the orinoco river is true.

A. IT FLOWS THROUGH ECUADOR

B. IT IS SECOND LONGEST RIVER IN SOUTH AMERICA

C. IT FLOWS THROUGH VENEZUELA

D. IT EMPTIES INTO THE PACIFIC OCEAN

Answers

It's C: It flows through Venezuela

Answer:

C. IT FLOWS THROUGH VENEZUELA

Explanation:

correct asnwer

Which of the following gases will diffuse most quickly at a given temperature?

Gas A; MW = 14.28 g/mol

Gas B; MW = 26.92 g/mol

Gas C; MW = 39.95 g/mol

Gas D; MW = 108.60 g/mol

Answers

Gas A; MW = 14.28 g/mol

The gas that is having lowest density will diffuse faster than other gases. As lesser denser will diffuse more quickly than the one which is more denser. Density is directly proportional to mass of the substance that is more mass of the substance is , more denser it will be. So here the Gas A is having lesser molecular weight than the other gases so it will diffuse more quickly than the other gases.

Gas A; MW = 14.28 g/mol

A soda has a volume of 560 ml and a density of 3.2g/ml. what is the mass?

Answers

Answer: 1792 g or 1.792 kg

Reason:
We know that,
Density = [tex] \frac{Mass}{Volume} [/tex]

Given: Volume = 560 ml, Density = 3.2 g/ml.

Therefore, Mass = Volume x Density
                           = 560 x 3.2
                           = 1792 g
                           = 1.792 kg

Thus, mass of 560 ml soda, having density of 3.2g/ml is 1792 g.

Answer: Mass of the substance is 1.792 kg

Explanation: Density of a substance is defined as the mass contained per unit volume.

[tex]Density=\frac{mass}{volume}[/tex]

Given:

Volume = 560 ml

Density = 3.2 g/ml

[tex]Mass=Density\times volume[/tex]

[tex]Mass=3.2g/ml\times 560ml=1792g[/tex]

Mass of the substance is 1792 g or 1.792 kg.

The equation 2c3h7oh(g) + 9o2(g)→6co2(g) + 8h2o(g) is an example of which type of reaction?

Answers

 the answer is combustion


The given equation represents a combustion reaction. The organic gas combines with atmospheric oxygen to form carbon dioxide and water .

What is combustion?

Combustion is a type of reaction, in  which gaseous reactants combines with atmospheric oxygen to form carbon dioxide and water. In combustion reaction heat energy is released by the reaction system.

The reaction from which a heat energy is released is called an exothermic reaction. Thus, combustion is an exothermic reaction. The reaction in which heat is absorbed the system is called endothermic reaction.

In the given reaction, 2 moles of propanol reacts with 9 moles of oxygen forming 6 moles of carbon dioxide and 8 moles of water. This reaction is an example of combustion.

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Which of the following best explains why you sanded the copper wire before burning it?
to create less friction between the copper and the tongsto make sure that copper metal was exposed on the surface of the wireto make the copper wire flammableto weaken the copper wire so it would be more reactive

Answers

Answer: Option (b) is the correct answer.

Explanation:

When copper wire is place into the atmosphere or anywhere then there is possibility that some oxide layer or impurity must have deposited over its surface.

So, when we sanded copper wire then these impurities get removed and copper metal gets exposed onto the surface.

Thus, we can conclude that you sanded the copper wire before burning it to make sure that copper metal was exposed on the surface of the wire.

Answer:

B. to make sure that copper metal was exposed on the surface of the wire

Explanation:

Right on Edgen.

Kasterville is a rapidly growing city. Which of the following situations will most likely have a positive impact on the resources available to Kasterville? A. Factories dump wastewater directly into nearby rivers. B. Builders cut down trees to build homes without replanting new ones. C. Most people water their lawns every day to keep them green. D. Most people are careful to recycle all glass, metal, and plastic.

Answers

D. Most people are careful to recycle all glass, metal, and plastic.

Answer: D

Explanation:

What is the IMA of the following pulley system?


2
3
4
5

Answers

I think  the answer is five 

Option D: 5

IMA is Ideal Mechanical advantage, for pulley system it is equal to the number of ropes present in the system. At ideal conditions, it is equal to the number of times, input force is getting multiplied. For example, If a pulley uses two ropes, its required mechanical force to displace the load will be divided into two or the distance that should be pulled will be multiplied by two (keeping total energy constant).

In the pulley system in diagram, there are total of 5 ropes in the system that is total strand that lead directly to the load thus, IMA for this pulley system will be 5.


Yes or no: will a precipitate form when solutions of ba(no3)2 and koh are mixed?

Answers

No, a precipitate will not form when barium nitrate, Ba(NO3)2, reacts with potassium hydroxide, KOH, in aqueous solution because both products are soluble in water.

How many phases of matter are present in whipped cream?

Answers

I think it has three phases, that is solid phase, liquid phase and gas phase.
Whipped cream is a colloid. It consists of a gas in a liquid, so it is a foam. The solution is a colloidal suspension with solid particles in a liquid. 

which describes the force between two magnets winter south poles are almost touching

Answers

the correct answer i believe is frcition

I believe it's  the poles strongly repel each other.

If you don't reply with an actual answer I will report it and you will be reported and itll give me back my points
1.If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12
liters, what is the temperature?
2.If I have an unknown quantity of gas at a pressure of 121.6 kPa, a
volume of 31 liters, and a temperature of 87 0C, how many moles of
gas do I have?
3.If I contain 3 moles of gas in a container with a volume of 60 liters and
at a temperature of 400 K, what is the pressure inside the container?
4.If I have 7.7 moles of gas at a pressure of 0.09 atm and at a temperature
of 56 0C, what is the volume of the container that the gas is in?
5.If I have 17 moles of gas at a temperature of 67 0C, and a volume of
88.89 liters, what is the pressure of the gas?
Use Dalton’s Law of Partial Pressures and Grahams law of effusion to solve
the following problems:


6.At a certain temperature, molecules of methane gas, CH4 have an average
velocity of 0.098 m/s. What is the average velocity of carbon dioxide
molecules at this same temperature?
7.7.) Find the relative rate of diffusion for the gases chlorine, Cl2 and ethane,
C2H6.
8.495 cm3 of oxygen gas and 877 cm3 of nitrogen gas, both at 25.0 °C and
114.7 kPa, are injected into an evacuated 536 cm3 flask. Find the total
pressure in the flask, assuming the temperature remains constant.

Answers

i think its number 5 

Using the example reaction aA + bB → cC + dD write the potential first order and second order rate laws

Answers

Given the equation aA + bB → cC + dD, which is an irreversible reaction, the most common rate laws are the product of the concentration of the reactants, each raised to a power.

This is the the general form of such laws.

r = K [A]^m * [B]^n

The order of the reaction is the sum of the exponents: m + n.

For first order reaction m+ n = 1, yields to the next potential laws:

m = 1, n = 0 => r = k [A]
m = 0, n = 1 => r = k [B]
m=0.5, n = 0.5 => r = [A]^0.5 [B]^0.5

And other combinations where the sum of the exponents are 1.

For second order reactions, m + n = 2, these are some potential laws:

m = 1, n = 1 => r = k[A][B]
m=0, n = 2 => r = k[B]^2
m=2, n = 0 => r = k[A]^2

m=1.5, n = 0.5 => r = k[A]^1.5 [B]^0.5

As you see there are many potential laws all of them with the form

r = [A]^m [B]^n, being the order of the reaction m + n

Final answer:

The potential first-order rate law is rate = k[A] or rate = k[B], and the potential second-order rate law is rate = k[A][B].

Explanation:

The potential first-order rate law for the given reaction aA + bB → cC + dD is rate = k[A] or rate = k[B]. This means that the rate of the reaction is directly proportional to the concentration of either reactant A or reactant B.

The potential second-order rate law for the given reaction is rate = k[A][B]. This indicates that the rate of the reaction depends on the product of the concentrations of both reactant A and reactant B.

which element would be a positive ion in a compound: Sr or Te

Answers

The element that would be a positive ion in a compound between Sr and Te would be Sr.

How to determine the charge on ions

Elements form positive or negative ions based on the number of valence electrons their atoms contain and the tendency to either donate these electrons to form bonds or accept more electrons to form bonds.

The donation of acceptance of electrons will enable atoms to form an octet structure.

The number of valence electrons in Sr atoms is 2. In order to form an octet when bonding, these 2 electrons are readily donated rather than accepting more electrons. Thus, Sr ions are usually [tex]Sr^{2+[/tex].

The number of valence electrons in Te atoms is 6. Hence, instead of donating these electrons to form an octet, it will rather accept 2 more electrons. Thus, Te ions are usually [tex]Te^2^-[/tex].

In other words, Sr would be the positive ion in a compound.

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Final answer:

Strontium (Sr) would form a positive ion in a compound since it is an alkaline earth metal that readily loses electrons to become a cation, whereas tellurium (Te) tends to gain electrons to form an anion.

Explanation:

Between the elements strontium (Sr) and tellurium (Te), Sr would typically form a positive ion in a compound. This is because Sr is an alkaline earth metal and is found in Group 2 of the periodic table, where elements readily lose electrons to form cations with a +2 charge. On the other hand, Te is a metalloid in Group 16, known for gaining electrons to form anions with a -2 charge. Compounds are neutral, which means that the total number of positive charges must balance the total number of negative charges.

Additionally, Sr is lower down in its group than Ca, making it easier to remove an electron from Sr than from Ca. Hence, Ca has the higher ionization energy (IE) compared to Sr. When considering a potassium ion (K+), it would also be harder to remove an electron because it already has a positive charge. Therefore, the IE of K+ is significantly higher, especially since the next electron to be removed would come from a different electron shell.

"which common material is an example of a polymer?"

Answers

The answer is plastic...

Hope this helps.

Addition of a benzopyrene adduct is the result of what type of reaction?

Answers

alkylation reaction
hope it helped give thanks :)

All chemical reactions involve a transfer of energy true or false

Answers

Answer is: true.
For all chemical reaction some energy is required and that energy is called activation energy (energy that needs to be absorbed for a chemical reaction to start). There are two types of reaction: endothermic reaction (chemical reaction that absorbs more energy than it releases) and exothermic reaction (chemical reaction that releases more energy than it absorbs).

Answer:

true

Explanation:

What is the experimental molar heat of combustion?

Answers

Explanation:

Molar heat combustion:

Molar heat of combustion is defined as heat released when 1 mole of substance is burnt under the action of oxygen gas to give water and carbon-dioxide.It is measured in kiloJoules (kJ) per mole.This heat of energy can be positive or negative.

If the enthalpy is positive than the reaction is said to be an endothermic reaction.If the enthalpy is negative than the reaction is said to be an exothermic reaction.

The molar heat of combustion is illustrated as the heat discharged when one mole of the component is burnt by reacting with oxygen gas to provide carbon dioxide and water. It is determined in kJ per mole. This heat of energy can be negative or positive. In case if the enthalpy is negative than the reaction is considered as an exothermic reaction, and if the enthalpy is positive than the reaction is considered as an endothermic reaction.

What does the suffix -ide indicate when naming an ionic compound?

Answers

it means it's the anion or the negatively charged atom

explain why it is often milder in areas such as coastal Maryland while areas such as Kansas or Iowa have more extremes in temperature?

Answers

Final answer:

Coastal areas like Maryland have milder climates due to the moderation by nearby ocean water, which has a stable temperature that influences the air temperature over land. In contrast, inland areas such as Kansas and Iowa experience more extreme temperatures due to their distance from the ocean's moderating effects and greater influence from continental air masses.

Explanation:

The location of an area relative to the coast significantly influences its climate due to the effects of oceanality and continentality. Coastal Maryland, being near the Atlantic Ocean, experiences milder conditions because the temperature of ocean water remains relatively stable throughout the year, moderating the air temperature over the land. In contrast, inland areas such as Kansas and Iowa are subject to more extreme temperatures due to their distance from the ocean's moderating influence, leading to significantly warmer summers and colder winters.

Ocean water has a high heat capacity, which means it absorbs and releases heat more slowly than land, resulting in a smaller range of temperature fluctuations. This heat inertia is why coastal areas tend to have more moderated climates. For example, airflow from the ocean keeps San Francisco's climate mild and more constant throughout the year, while Salt Lake City, which is an inland city at approximately the same latitude, experiences greater temperature variation.

In summary, coastal regions are influenced by the temperature of the nearby ocean, which changes little with the seasons. This results in a milder climate with less variation between summer and winter temperatures. Conversely, inland regions are more subject to continental air masses, leading to a larger range in temperatures and more extreme seasonal conditions.

Which substance produced in the laboratory is used as a post exposure preventative measure against rabies?

Answers

I think the answer is synthetic immunoglobulins: Immunoglobulins are also called antibodies, they are glycoproteins molecules produced by plasma cells (white blood cells). They act as the critical part of the immune response by specifically recognizing and binding to particular antigens, such as bacteria and viruses, and enhancing their destruction. Synthetic immunoglobulins may differ in structure to that of an antibody and can be generated either from nucleic acids, as in the case of aptamers, or from non-immunoglobulin protein scaffolds/peptide aptamers, into which hypervariable loops are inserted to form the antigen binding site.

Pellets of calcium chloride are spread on a sidewalk covered in water that is 36°c. under which circumstance will the calcium chloride dissolve faster? it rains, increasing the amount of water on the sidewalk. sand is sprinkled on the sidewalk. the water cools to a temperature of 33°c. people walking on the sidewalk crush the calcium chloride pellets. the air pressure increases as the weather changes.

Answers

It is the fourth answer, " People crush them when they walk on them" Hope this helps!

Answer:

people walking on the sidewalk crush the calcium chloride pellets.

Explanation:

When calcium chloride pellets are crushed with feet it increases the surface area of the calcium chloride. As the surface area increase the number of collision between the reactant molecules increases. Here the reactant molecules are calcium chloride ions and water molecules. In the process of dissolution the calcium chloride ions get hydrated by the dipoles of the water molecules. As the frequency of collision increases it lowers the activation energy or threshold barriers to start a reaction.  

Please help with a chem question thank you!

Answers

I Believe it is A FOR THE correct answer

What mineral has the least hardness according to the scale?

Answers

The softest mineral in the Mohs Hardness Scale is talc.
Talc is often used in baby powder and corn starch, among other things. Talc cleaves into thin sheets, and it is held together only by van de Waals bonds, which allows these sheets to slip past each other. This gives the mineral its softness and it is often valued as a high-temperature lubricant.

When ammonium nitrate is dissolved in water, energy is absorbed from the surroundings, causing a decrease in the resulting solution's temperature. Which of the following best describes this type of reaction?

Answers

A reaction that absorbs energy from the solution and decreases the solution's temperature is called and endothermic reaction. A physical change that absorbs heat can also be described as endothermic.
The opposite of endothermic is exothermic. A reaction that is exothermic releases energy to the surroundings. This is observed as an increase in the temperature of the solution.

A 250 mL sample of a .125 M solution of NaOH contains _____g of NaOH

Answers

Hello!

A 250 mL sample of a 0,125 M solution of NaOH contains 1,25 g of NaOH

To calculate that, we use the definition of molar concentration (M=moles/L) and the solution volume in L to get the moles of NaOH in the solution. After that, we get the mass of NaOH from the molar mass. All these calculations are shown in the following conversion factor:

[tex]MassNaOH=250mLsol* \frac{1L}{1000mL}* \frac{0,125 mol NaOH}{1 Lsol}* \frac{39,997 g NaOH}{1 mol NaOH} \\ =1,25gNaOH [/tex]

If the half-life of a radioactive isotope is 5,000 years, how much of the radioactive isotope in a specimen will be left after 10,000 years?

Answers

10,000÷5,000=2 which means the amount of radioactive isotope has reduced by half twice. so, 25% of the starting amount of radioactive isotope will be left.

Final answer:

After two half-lives of 5,000 years each, only 25% of the original radioactive isotope would remain.

Explanation:

If the half-life of a radioactive isotope is 5,000 years, after 10,000 years, two half-lives will have passed. According to exponential decay, after the first half-life, 50% of the original isotope remains. After the second half-life, another half of this remaining amount will have decayed, leaving only 25% of the original isotope. We can use the expression (1/2)n, where 'n' is the number of half-lives, to calculate the remaining amount of the isotope. In this case, it would be (1/2)2 = 1/4 or 25%.

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