he half-life of cesium-137 is 30 years. Suppose we have 130-mg sample. (a) Find the mass that remains after t years.

Answers

Answer 1

To find the mass that remains after t years, we can use the formula:

Mt = M0 * e^(-λt)

where M0 is the initial mass, λ is the half-life of the substance, and t is the number of years.

In this case, the initial mass is 130 mg, and the half-life of cesium-137 is 30 years. So, we can set up the equation:

M0 = 130 * e^(-0.30t)

We want to find the mass that remains after 20 years, so we can substitute t = 20 into the equation:

M0 = 130 * e^(-0.30*20)

Now we can solve for M0:

M0 = 130 * e^(-0.60)

M0 = 130 * e^-0.60

M0 = 130 * 0.515

M0 = 69.35 mg

So after 20 years, approximately 69.35 mg of cesium-137 will remain.

To find the mass that remains after t years, we can simply plug t into the formula:

Mt = 130 * e^(-0.30t)

For example, to find the mass that remains after 30 years, we can substitute t = 30:

M30 = 130 * e^(-0.30*30)

M30 = 130 * e^(-0.90)

M30 = 130 * 0.815

M30 = 106.23 mg

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Related Questions

Identify a minimum of six properties that are unique to water.
State how the structure of a water molecule and its bonds relate to each property.

Answers

Answer:

1)Boiling Point and Freezing Point.

2)Surface Tension, Heat of Vaporization, and Vapor Pressure.

3)Viscosity and Cohesion.

4)Solid State.

5)Liquid State.

6)Gas State.

Explanation:

Water molecules are polar, so they form hydrogen bonds. This gives water unique properties, such as a relatively high boiling point, high specific heat, cohesion, adhesion and density.

Answer:

Hey I have the same project do you think you can send it to me please :)

Explanation:

i need assistance with chemistry

i need assistance with chemistry

Answers

Answer:

K3N

Explanation:

here is a hint.

K has a positive charge of 1

and n has a negative charge of 3

K1 and N3

all you do is flip both sides to

K3 N1

get rid of 1

If it was a charge of 2 or any number higher keep it (K3N2)

If both positive charge and negative charge was the same number, get rid of both numbers (KN)

PLEASE HELP!!!!
it would mean alot ! ​

PLEASE HELP!!!! it would mean alot !

Answers

Answer:

i looked it up its slinky waves

Explanation:

Answer:

diffracted

Explanation:

Sure it might look like a slinky but if you're talking about waves then it's deffinetly diffracted hope this helps

Work out the empirical formula of a compound that contains 35% of nitrogen , 5% of hydrogen and 60% of oxygen.

Answers

Answer:

\(H_5N_5O_6\)

Explanation:

Hello there!

In this case, for the determination of empirical formulas, it is firstly necessary to assume the given percentages of the constituent atoms as the masses so we can compute their moles in the formula:

\(n_N=\frac{35gN}{14.01g/mol} =2.5molN\\\\n_H=\frac{5g}{1.01 g/mol}=5molH\\\\n_O=\frac{60g}{16 g/mol} =3molO\)

Thus, we need to divide the resulting moles, by the fewest ones (those of nitrogen) in order to determine the coefficients in the formula:

\(N:\frac{2.5}{2.5}=1\\\\H:\frac{5}{2.5}=2\\\\O:\frac{3}{2.5} =1.2\)

However, we need to turn all these numbers, whole numbers, so we multiply by 5 to get:

\(H_5N_5O_6\)

Best regards!

A solution formed from the dissociation of calcium sulfate, caso4. determine the molar solubility of this salt.

Answers

The molar solubility of CaSO4 in the solution is approximately 4.9 × 10⁻³ mol/L.

The dissociation of calcium sulfate, CaSO4, in water results in the formation of calcium ions, Ca2+, and sulfate ions, SO42-. The balanced chemical equation for this dissociation is:

CaSO4(s) ⇌ Ca2+(aq) + SO42-(aq)

To determine the molar solubility of this salt, we need to find the concentration of the ions in the solution at equilibrium. Let's assume that x mol/L of CaSO4 dissociates, which means that the concentration of Ca2+ and SO42- ions in the solution will also be x mol/L.

Using the balanced chemical equation, we can set up an expression for the solubility product, Ksp, which is the product of the concentrations of the ions raised to their stoichiometric coefficients:

Ksp = [Ca2+][SO42-] = x^2

The Ksp for calcium sulfate is 4.93 x 10^-5 at 25°C, so we can solve for x:

4.93 x 10^-5 = x^2

x = 2.22 x 10^-3 mol/L

Therefore, the molar solubility of calcium sulfate is 2.22 x 10^-3 mol/L.
Hi! To determine the molar solubility of calcium sulfate (CaSO4) in a solution, you need to consider its solubility product constant (Ksp). The Ksp value for CaSO4 is 2.4 × 10⁻⁵. When CaSO4 dissociates in water, it forms calcium ions (Ca²⁺) and sulfate ions (SO₄²⁻).

The balanced dissociation equation is:
CaSO4(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq)

Assuming molar solubility of CaSO4 is 's' mol/L, the concentration of Ca²⁺ and SO₄²⁻ ions in the solution would also be 's' mol/L. The Ksp expression can be written as:

Ksp = [Ca²⁺][SO₄²⁻] = (s)(s) = s²

Now, plug in the Ksp value to solve for 's':

2.4 × 10⁻⁵ = s²
s = √(2.4 × 10⁻⁵) ≈ 4.9 × 10⁻³ mol/L

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Mixtures:

(A) Have specific compositions
(B) do not have specific compositions
(C) are made from liquids
(D) are made from one substance

Answers

The true statement about mixtures is that they do not have specific compositions (option B).

What is a mixture?

Mixture is a substance made up of two or more chemical components that are not chemically linked.

This further means that the constituents of a mixture maintain or keep their individual chemical identities because there is no breaking of bonds.

As opposed to mixtures, compounds are made up of constituents that are chemically bonded to one another, hence, possess a definite composition.

Examples of mixtures are as follows:

Sugar and waterSalt and waterAir (mixture of gases)Salt and sugarSand and waterOil and water

Therefore, the true statement about mixtures is that they do not have specific compositions.

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Which atoms are in all carbohydrates?

Answers

Carbohydrates require carbon as their primary component. There is carbon in every known carbohydrate. All carbohydrates also contain hydrogen and oxygen atoms, with the exception of a few simple sugars, which only contain carbon and hydrogen atoms.

Carbon, hydrogen, and oxygen atoms make up the macromolecules known as carbohydrates. They are a significant energy source. They can be found in fruits and vegetables as sugars, starches, and fibre. What categories do the carbs fit into? Starchy meals are complex carbohydrates because they include two or more sugar units. Compared to simple carbs, complex carbohydrates' molecules digest and transform more slowly. They are widely distributed in whole-grain bread, cereals, lentils, beans, peanuts, potatoes, peas, and corn. As one of the three primary macronutrients, carbohydrates are one of the three.

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How many atoms are in 34.2 grams of carbon?

Answers

Answer:

6.02*1022

Explanation:

I don't know why

a solution is prepared by adding 1.00 x 102 ml of 0.50 m hcl to a 1.00 x 102 ml solution that is 0.10 m in h2s and 0.50 m in hs-. what type of acid base problem do you have to solve for the ph?Think carefully about this one and consider the number of moles of each species you have in solution.

Answers

This type of problem is an acid-base neutralization problem. When hydrochloric acid (HCl) is added to a solution that contains both hydrogen sulfide (H2S) and hydrosulfide (HS-), a neutralization reaction takes place between the HCl and H2S, leading to the formation of sulfuric acid (H2SO4) and water.

The reaction can be represented as:

HCl + H2S -> H2SO4 + H2O

To find the pH of the resulting solution, we need to calculate the concentration of hydrogen ions (H+) in the solution, which is determined by the dissociation of sulfuric acid and the remaining HCl. The pH can then be calculated using the definition of pH as the negative logarithm of the hydrogen ion concentration. This requires a multi-step calculation, taking into account the initial concentration of the reactants, the stoichiometry of the reaction, and the changes in concentration that occur as a result of the reaction.

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Element x is in group 2, and element y in group 7, of the periodic table. Which ions will be present in the compound formed when x and y react together?.

Answers

The reaction of elements x from group 2 with elements from group 7 of the periodic table will produce a compound where both cations and anions are present.

Group 2 elements

This group makes up the so-called alkaline earth metals and is made up of: beryllium, magnesium, calcium, strontium, barium and radium.

Elements of group 7

These elements make up what is called the manganese family and have the particularity of being metals with 7 valence electrons.

The valence electrons of manganese and its family of elements are distributed 2 in the last shell and 5 in the penultimate shell.

Compounds formed by manganese and alkaline earth

An example of a compound formed by manganese and alkaline earth is calcium permanganate. It is an oxidizing agent that is formed by a metallic cation of calcium and two anions of permanganate.

These compounds formed are powerful oxidants, which, even when they do not produce combustion, can accelerate that of other materials, leading to the formation of explosive mixtures.

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Element x is in group 2, and element y in group 7, of the periodic table. Which ions will be present

What is the gravitational potential energy of a box that is 2.9 m off the ground and a mass of 12.5 kg? * 20 points

Answers

Answer:

362,5J

Explanation:

formula for calculating Gravitational Potential Energy is mass×gravitational field strength ×height

12.5×10×2.9=362,5J

2 AgNO3(aq) + K2SO4(aq) → 2 KNO3(aq) + Ag2SO4(s) The net ionic reaction for the balanced equation shown above is? a. K+ + NO 3 - KNO3 b. 2K+ + 30% - K2SO4. c. 2Ag+ + so - Ag2SO4. d. H+ + OH -- H2O.

Answers

Option C. 2Ag+ + SO42- --> Ag2SO4 is the The net ionic reaction for the balanced equation.

Mass and charge must be equal in net ionic equations. By balancing by mass, one may make sure that each element is present in equal amounts on both the product and reactant sides. Making ensuring that the total charge is the same on both sides of the equation is known as balancing by charge. A chemical equation for a process known as the net ionic equation only includes the species that are really involved in the reaction. In double displacement reactions, redox reactions, and acid-base neutralization processes, the net ionic equation is frequently employed.

The complete question is :

The net ionic reaction the balanced equation shown above is

2AgNO3 (aq) +K2SO4 (aq) --> 2KNO3 (aq)+ Ag2SO4 (s)

A. Ag+ + NO3- --> AgNO3

B. H+ + OH- --> H2O

C. 2Ag+ + SO42- --> Ag2SO4

D. 2K+ +SO4(2-) -->K2SO4

E.K+ +NO3- -->KNO3

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please help me i need yall will mark brainliest and 30 points!

please help me i need yall will mark brainliest and 30 points!

Answers

Reaction

2Fe(OH)₃ + 3H₂SO₄⇒Fe₂(SO₄)₃ + 6H₂O

because the limiting reactant is Fe(OH)₃, then the moles of all compounds will be based on moles of Fe(OH)₃

mole H₂SO₄ = 3/2 x mole Fe(OH)₃ = 3/2 x 3 mole = 4.5 mole

remaining mole of H₂SO₄ (as an excess reactant) = 6.4 - 4.5 = 1.9 mole

why do you have to heat the unknown copper chloride hydrate in this experiment?

Answers

In this experiment, the unknown copper chloride hydrate needs to be heated in order to remove the water molecules that are bound to the copper chloride compound. This process is called dehydration and it is necessary because we want to determine the exact mass of the anhydrous copper chloride compound.

By heating the sample, the water molecules are driven off and we are left with only the anhydrous copper chloride. This allows us to accurately measure the mass of the copper chloride compound without the interference of water molecules. Additionally, it is important to note that different hydrates have varying numbers of water molecules bound to them, so it is crucial to remove the water to obtain accurate and consistent results.

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help I would really appreciate it tyy!!

help I would really appreciate it tyy!!

Answers

Answer:

This image attached should help:

Explanation:

The reason that food web contains all organisms is because it shows every relationship, where food chain shows a more basic one. And the reason that they both have producers, consumers, and decomposers, is because they bothat least highlight a part of the almost every aspect, although it leans more to food web.

help I would really appreciate it tyy!!

here's the answer to the question in the image, I couldn't comment on the right question because a bot already did.

1. ant, love

active

2. dog, man

dormant

3. bug, ring

burning

4. dress, up

pressure

5. think, tiger

trinker

help I would really appreciate it tyy!!


Which of these elements is the odd one out? Li Na Mg K Rb Cs

Answers

Mg because it’s the only one that isn’t a alkali metal

Balance the following chemical equation

Balance the following chemical equation

Answers

Answer:

Explanation:

4). Ca(NO₃)₂ + Na₂SO₄ → CaSO₄ + 2Na(NO₃)₂

  This question is incorrect.

  Since, the final product by reacting Na⁺⁺ and NO₃⁻⁻ is NaNO₃

  Correct equation will be,

  Ca(NO₃)₂ + Na₂SO₄ → CaSO₄ + 2NaNO₃

  This equation is in the balanced form.

5). Ni(NO₃)₂ + KI → NiI + 2K(NO₃)₂

  Correct equation will be,

  Ni(NO₃)₂ + KI → NiI₂ + 2KNO₃

  [Since final product by reacting Ni⁺⁺ and I⁻ is NiI₂]

  Balanced form of this equation will be,

  Ni(NO₃)₂ + 2KI → NiI₂ + 2KNO₃

6). Ni(NO₃)₂ + KOH → NiOH + K(NO₃)₂

   Correct form of the equation will be

   Ni(NO₃)₂ + KOH → Ni(OH)₂ + KNO₃

   [Since reaction of Ni⁺⁺ and OH⁻ gives Ni(OH)₂ and the reaction of K⁺ and NO₃⁻ gives KNO₃]

   Now balancing this equation,

   Ni(NO₃)₂ + KOH → Ni(OH)₂ + 2KNO₃

                              ↓

  Ni(NO₃)₂ + 2KOH → Ni(OH)₂ + 2KNO₃

Which of the following is a compound?

A. Ne
B. N2
C. NaCl
D. O2

Answers

Answer:

C

Explanation:

Answer:

NaCl

Explanation:

Because it's sodium chloride


Set up and solve a system of linear equations to balance the
following chemical reaction:
Limestone, CaCO3, neutralizes the acid, H3O, in acid rain by the
following unbalanced equation:
H3O + CaCO3 yields
→ H2O+Ca+CO2

Answers

A system of linear equations to balance the following chemical reaction:

Limestone, CaCO₃, neutralizes the acid, H₃ O, in acid rain is:

2H₃O + CaCO₃ → 3H₂O + Ca + CO₂

To balance the chemical equation:

H₃O + CaCO₃ → H₂O + Ca + CO₂

We need to ensure that the number of atoms of each element is the same on both sides of the equation.

Let's assign variables to the coefficients of each compound:

H₃O: x

CaCO₃: y

H₂O: z

Ca: a

CO₂: b

Now, we can set up the system of equations based on the number of atoms for each element:

For hydrogen (H):

3x = 2z

For oxygen (O):

3x + 3y = 2z

For calcium (Ca):

y = a

For carbon (C):

y = b

For calcium (Ca):

a = 1

Solving this system of equations will give us the balanced coefficients. Let's solve it:

From the equation y = a, we have y = 1.

From the equation y = b, we have b = 1.

Substituting b = 1 into the equation 3x + 3y = 2z, we have:

3x + 3 = 2z

From the equation 3x = 2z, we have x = (2/3)z.

Substituting x = (2/3)z into the equation 3x = 2z, we have:

3(2/3)z = 2z

2z = 2z

This equation is true for any value of z, indicating that z can take any value.

Therefore, we can choose z = 3 to simplify the coefficients:

x = (2/3)z = (2/3)(3) = 2

y = 1

z = 3

a = 1

b = 1

Thus, the balanced equation is:

2H₃O + CaCO₃ → 3H₂O + Ca + CO₂

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What are the main organs for the respiratory system?

Answers

Answer:

lungs and blood vessels, airway

Explanation:

because the respiratory system are a system that helps people breate. the lungs breathe in oxygen and then breathe out carbon dioxide. the blood vessels carries the oxygen into the body to other part of the system in the body that needed oxygen to make glucose.

what is(are) the most plausible parameter value(s) for the alternative model given the observations? derive the mle(s) formula(ae). (you do not need to calculate the value(s).) enter in terms of (type g i) and (type t i).

Answers

The correct answer is

A reasonably straightforward technique for creating an estimate for an unknown parameter is maximum likelihood (MLE).

Assume that the random variables X1, , and Xn make up a random sample from the distribution f(x|); f(x|) is a point mass function for continuous random variables and a pdf for discrete random variables, respectively. We use the sign — to denote the fact that the distribution also depends on the parameter, which might be either a single parameter or a vector of parameters with real values. We define f(x1, , xn|) = f(x1|) f(xn|) for each observed random sample x1, , xn (1)

The joint probability is f(x1, , xn|) if f(x|) is pmf and the joint density function is f(x1, , xn|) if f(x|) is pdf. The likelihood function is now denoted by the notation f(x1, , xn|). As can be seen, the unknown parameter affects the likelihood function.

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A balloon with a volume of 2.0 l at 25°c is placed in a hot room at 35°c. the pressure on the balloon is constant at 1.0 atm. formula to use: v1 t1 = v2 t2 how does the volume of the balloon change after moving it to the hot room?

Answers

The volume increases and the final volume is 2.1 L

Why volume increases?

The volume of a gas is directly related to the heat and pressure. If temperature increases, volume increases.

If pressure increases, volume decreases

Based on Boyle's law,

The absolute temperature of a gas is directly proportional to the volume of the gas.

As the balloon change increases its temperature, the volume increases

The Boyle's equation is:

V₁T₂ = V₂T₁

Where,

V is volume T is absolute temperature of 1, initial state and 2, final state of the gas.

Replacing :

V₁ = 2.0L

T₂ = 35°C + 273.15 = 308.15K

V₂ = ?

T₁ = 25°C + 273.15 = 298.15 K

2.0L x 308.15 K = V₂ x 298.15 K

2.1 L = V₂

Final volume is 2.1L

Hence, The volume increases and the final volume is 2.1 L

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Answer:

increases, 2.1

Explanation:

I got it right.

How do you use the the word tentative in your own sentence?

Answers

Answer:

The time of the party is tentative and subject to change.Due to the storm, the plane's arrival time is tentative.The employees were not happy when they learned their pay raises were tentative and could be cancelled at any moment.

Explanation:

hope this helps

brainliest plz

use the following information to calculate δh∘f for h2so4(aq) in kj/mol . s(s) o2(g)→so2(g)δh∘=−296.8kj so2(g) 12o2(g)→so3(g)δh∘=−98.9kj [for h2o(l),δh∘f=−285.8kj/mol ].

Answers

The ΔH°f for \(H_2SO_4\)(aq) is -967.3 kJ/mol.

The balanced equation for the formation of \(H_2SO_4\)(aq) can be represented as follows:

2\(H_2\)(g) + \(O_2\)(g) + 2\(SO_2\)(g) + 2\(H_2O\)(l) → \(H_2SO_4\)(aq)

Now, let's calculate ΔH°f for \(H_2SO_4\)(aq) using the given information:

ΔH°f(\(H_2SO_4\)) = 2 × ΔH°f(\(H_2O\)) + ΔH°f(\(SO_2\)) + ΔH°f(\(O_2\)) - ΔH°f(\(SO_2\))

Substituting the given values:

ΔH°f(\(H_2SO_4\)) = 2 × (-285.8 kJ/mol) + (-296.8 kJ/mol) + (-98.9 kJ/mol) - 0

Simplifying:

ΔH°f(\(H_2SO_4\)) = -571.6 kJ/mol - 296.8 kJ/mol - 98.9 kJ/mol

= -967.3 kJ/mol

A balanced equation is a chemical equation that represents a chemical reaction in which the number of atoms of each element is the same on both sides of the equation. It follows the law of conservation of mass, which states that matter cannot be created or destroyed during a chemical reaction, only rearranged.

A balanced equation consists of reactants on the left side of the arrow, indicating the substances that participate in the reaction, and products on the right side, representing the substances formed as a result of the reaction. Coefficients are used to balance the equation by adjusting the number of molecules or atoms involved.

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Remember, the graph in question 1 is a cooling curve. A substance is
changing from a gas to a liquid to a solid. Which model illustrates the
final phase change in this cooling curve?
A) Image A
B) Image B
C) Image C
D) Image D

Remember, the graph in question 1 is a cooling curve. A substance ischanging from a gas to a liquid to

Answers

I think it’s c not sure

extend the left chain as far as the simulation allows. what is the base name for an ester with a propyl group attached to the carbonyl carbon atom?

Answers

The base name for an ester with a propyl group attached to the carbonyl carbon atom is "propyl ester." In the context of a simulation, you would need to extend the left chain according to the given parameters within the simulation for the specific compound you are working with.

If we extend the left chain of an ester with a propyl group attached to the carbonyl carbon atom as far as the simulation allows, we would have the following structure:

CH3-(CH2)2-C(=O)-OR

Where R represents the rest of the ester molecule.The base name for an ester with a propyl group attached to the carbonyl carbon atom is propyl propanoate. This name is derived from the parent carboxylic acid, which is propanoic acid (also known as propionic acid), and the alcohol used to form the ester, which is propanol (also known as 1-propanol or n-propanol).The esterification reaction between propanoic acid and propanol yields propyl propanoate as the ester product, with the elimination of a molecule of water. The ester is commonly used as a flavor and fragrance ingredient in various food and cosmetic products.

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2.04 thermal and chemical change

Answers

Explanation:

thermal changes are those in which heat exchange is involved like endothermic and exothermic

while in chemical changes collision between the reactant occurs which result into product

2. Why is the mole important in chemistry?a. Because it always weighs the same amountb. Because it always counts the same number of itemsc. Because it can be weighed on a scale

Answers

The moles allow us to associate the microscopic scale of atoms to the macroscopic one to be able to make calculations of mass. The weight of a mole will depend on the element so it does not always weigh the same.

One mole will always represent 6.022x10^23 atoms according to Avogadro's number so the correct answer will be:

b. Because it always counts the same number of items

A chemistry student must write down in her lab notebook the concentration of a solution of sodium hydroxide. The concentration of a solution equals the mass of what's dissolved divided by the total volume of the solution. Here's how the student prepared the solution: The label on the graduated cylinder says: empty weight: She put some solid sodium hydroxide into the graduated cylinder and weighed it. With the sodium hydroxide added, the cylinder weighed . She added water to the graduated cylinder and dissolved the sodium hydroxide completely. Then she read the total volume of the solution from the markings on the graduated cylinder. The total volume of the solution was . What concentration should the student write down in her lab notebook? Be sure your answer has the correct number of significant digits.

A chemistry student must write down in her lab notebook the concentration of a solution of sodium hydroxide.

Answers

Answer:

1.099 gmL¯¹ ≈ 1.1 gmL¯¹

Explanation:

From the question given above, the following were obtained:

Mass of empty cylinder = 9.5 g

Mass Cylinder + NaOH = 31.92 g

Volume of solution = 20.4 mL

Concentration of solution =?

Next, we shall determine the mass of sodium hydroxide, NaOH. This can be obtained as as illustrated below:

Mass of empty cylinder = 9.5 g

Mass Cylinder + NaOH = 31.92 g

Mass of NaOH =?

Mass of NaOH = (Mass Cylinder + NaOH) – (Mass of empty cylinder)

Mass of NaOH = 31.92 – 9.5

Mass of NaOH = 22.42 g

Finally, we shall determine concentration of the solution as follow:

Mass of NaOH = 22.42 g

Volume of solution = 20.4 mL

Concentration of solution =?

Concentration = mass /volume

Concentration of solution = 22.42 / 20.4

Concentration of solution = 1.099 gmL¯¹ ≈ 1.1 gmL¯¹

Therefore, the concentration of the solution is 1.1 gmL¯¹

if
half life of C -14 is 5700 years. how many years pass a sample
decays from an activity of 1050 to an activity of 205

Answers

It will take approximately 18197 years for the sample of C-14 to decay from an activity of 1050 to an activity of 205.

The question is asking for the number of years that will pass before a sample of C-14 decays from an activity of 1050 to an activity of 205. Given that the half-life of C-14 is 5700 years, we can use the formula for exponential decay to solve for the time required. The formula is:
N = N₀ (1/2)^(t/t₁/₂)
where:
N = final amount
N₀ = initial amount
t = time elapsed
t₁/₂ = half-life
We can rearrange the formula to solve for t:
t = t₁/₂ (ln(N₀/N)) / ln(1/2)
Using the given values, we have:
N₀ = 1050
N = 205
t₁/₂ = 5700
Substituting into the formula:
t = 5700 (ln(1050/205)) / ln(1/2)
t ≈ 18197 years (rounded to the nearest year)

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It will take approximately 18197 years for the sample of C-14 to decay from an activity of 1050 to an activity of 205.

The question is asking for the number of years that will pass before a sample of C-14 decays from an activity of 1050 to an activity of 205. Given that the half-life of C-14 is 5700 years, we can use the formula for exponential decay to solve for the time required. The formula is:

N = N₀ (1/2)^(t/t₁/₂)

where:

N = final amount

N₀ = initial amount

t = time elapsed

t₁/₂ = half-life

We can rearrange the formula to solve for t:

t = t₁/₂ (ln(N₀/N)) / ln(1/2)

Using the given values, we have:

N₀ = 1050

N = 205

t₁/₂ = 5700

Substituting into the formula:

t = 5700 (ln(1050/205)) / ln(1/2)

t ≈ 18197 years (rounded to the nearest year)

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