The half life of radium-226 is 1600 years.

a. After how many half-lives would 25% of the radium-226 remain.
b. Write a function m(t) that models the mass remaining after years.
c. How much of the sample will remain after 3000 years?
d. After how long will only 15 mg of the sample remain?

Answers

Answer 1

Answer:

Explanation:

a )

half life = 1600 years

50% in 1600 years

25% in next 1600 years

so 25% in total of 3200 years .

b )

disintegration constant = .693 / half life

= .693 / 1600

λ= 4.33 x 10⁻⁴ year⁻¹

m(t) = [tex]m_0e^{-\lambda t }[/tex]

m₀ is initial mass , λ =  4.33 x 10⁻⁴ year⁻¹

c )

m(t) after 3000 years , t = 3000

m(t) = [tex]m_0e^{-4.33\times10^{-4 }\times 3000 }[/tex]

= [tex]m_0e^{-1.3}[/tex]

= .2725 m₀

percentage of mass remaining = 27.25 %

Answer 2

25% radium-226 remain after 3200 years. 6.82 mg of sample remains after 3000 years. 15 mg of the sample will stay long about 1179. 19 years.

Half life of radium-226 = 1600 years

What is half-life?

half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

Calculation of each part can be done as

a )

half-life = 1600 years

50% in 1600 years

25% in next 1600 years

so 25% in total of 3200 years .

b )

Let decay function is

[tex]m(t) = m_o e^{-kt} \ \ \ \ \ ...(i)\\[/tex]

where k is decay constant

At half life,

[tex]m(t) = \frac{m_o}{2},t= 1600\ years\\So,\ \frac{m_o}{2} = m_oe^{-k1600}\\\frac{1}{2} = e^{-k1600}\\[/tex]

applying log on both sides

[tex]ln \frac{1}{2} = lne^{-1600k}\\-0.693147 = -1600 k \\k =\frac {0.693147}{1600}\\k = 4.332\times10^{-4}\\[/tex]

substitute the value of k in equation (i)

[tex]m(t) = m_oe^{-4.332\times10^{-4t}}\\m(t) = 25e^{-0.0004332t}[/tex]

c) when t = 3000 years

[tex]m(t) = 25e^{-0.0004332t}[/tex]

[tex]m(3000) = 25e^{-0.0004332\times3000}[/tex]

remain sample after 3000 years = 6.82 mg

d) when m(t) = 15 mg

[tex]15 = 25e^{-0.0004332t}\\e^{-0.0004332 t} = \frac{15}{25}\\applying\ log\ on\ both\ side\\ln \ e^{-0.0004332t}=ln(\frac{15}{25)}\\-0.0004332t = -0.510825\\t=\frac{0.510825}{0.0004332}\\t= 1179.19 \ years[/tex]

Hence, this is the required answer.

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Related Questions

A sample of compound contains 5.65x10 21 molecules molar mass of the compound is 89.06g/ mol determine the mass of the sample in grams

Answers

Answer:

Explanation:

no of molecules=5.65*10^21

NA=6.23*10^23

no of moles=no of molecules/avogadro number

no of moles=5.65*10^21/6.23*10^23

no of moles=9.07*10^-3

now we know that

no of moles=mass/molar mass

mass=no of moles*molar mass

mass=9.07*10^-3*89.06

mass=0.808 g

how many elements are present No and NO

Answers

For the first one No: 1
For the second one NO: 2

compare the size of I, I+ and I-

Answers

umm explanation pls so i answee

A. The chemical formula for iron (III) sulfate is Fe2(SO4)3. How many atoms of each element are present?

2 iron, 3 sulfur, 12 oxygen
3 iron, 3 sulfur, 12 oxygen
2 iron, 1 sulfur, 4 oxygen
6 iron, 3 sulfur, 12 oxygen
B.How many moles of hydrogen are in 1.8 mole(s) of quinine?

Express your answer using two significant figures.

C. How many moles of carbon are in 5.4 moles of quinine?

Express your answer using two significant figures.

D. How many moles of nitrogen are in 2.0×10−2 mole of quinine?

Express your answer using two significant figures.

Answers

Answer:

A. 2 Fe, 3 S and 12 O

B. 43 moles of H

C. 1.0×10² moles of C

Explanation:

A. Formula for iron (III) sulfate is Fe₂(SO₄)₃

This salt has 2 atoms of iron and 3 sulfates, so in total we have:

2 Fe, 3 S and 12 O

Pay attention to the subscripts

B. Formula for quinine is: C₂₀H₂₄N₂O₂

If we continue with the example before we can say that 1 mol of Iron (III) sulfate contains 2 moles of Fe, 3 moles of S and 12 moles of O

Then, 1 mol of quinine contains 24 moles of H

So 1.8 moles of quinine, may contain (1.8 . 24) /1 = 43 moles of H

C.  1 mol of quinine contains 20 moles of C

5.4 moles of quinine may contain (5.4 . 20) /1 = 1.0×10²

(As the answer must be in 2 significant figures and the real answer is 108, I had to use scientific notation)

5. What is the pH of an aqueous solution of the strong acid, Perchloric Acid (HClO4), with a concentration of 0.007 M?

Answers

Answer:

The pH is approximately: 2.1549

Explanation:

pH = - log(0.007)

Help me I’ll do anything

Answers

Answer:

its not A B or C soo choose D *This is what i think*

Answer:

A) something that causes physical pain

hope this helps

Explanation:

Which situation describes a chemical change?
A. Clay pressed into a mold takes on the shape of the mold.
B. Baking soda added to vinegar gives off carbon dioxide gas.
C. Chocolate changes from a solid to a liquid when heated.
D. Rubbing pencil lead onto paper changes the color of the paper.

Answers

Answer:

C

Explanation:

I just took the test

Answer:

B

Explanation:

2. Suppose 13.7 g of C2H2 reacts with 18.5 g O2 according to the reaction below. C2H2(g) + O2(g) → CO2(g) + H2O(ℓ) a. What is the mass of CO2 produced? b. What is the limiting reagent?

Answers

Answer:

Mass of CO₂ produced = 20.328 g

Oxygen is limiting reagent.

Explanation:

Given data:

Mass of C₂H₂ = 13.7 g

Mass of O₂ = 18.5 g

Mass of CO₂ produced = ?

What is limiting reagent = ?

Solution:

Chemical equation:

2C₂H₂ + 5O₂      →     4CO₂ + 2H₂O

Number of moles of C₂H₂:

Number of moles = mass /molar mass

Number of moles = 13.7 g/ 26.04 g/mol

Number of moles = 0.526 mol

Number of moles of O₂:

Number of moles = mass /molar mass

Number of moles = 18.5 g/ 32 g/mol

Number of moles = 0.578 mol

Now we will compare the moles of CO₂ with C₂H₂ and O₂

                      C₂H₂              :                CO₂

                           2                :                 4

                       0.526            :              4/2×0.526 = 1.052

                      O₂                  :                   CO₂

                        5                   :                     4

                      0.578             :                4/5×0.578 = 0.462

The number of moles of  CO₂ produced by O₂  are less thus oxygen will be limiting reactant.

Mass of CO₂ produced:

Mass = number of moles × molar mass

Mass = 0.462 mol × 44 g/mol

Mass = 20.328 g

What volume of a 0.181 M nitric acid solution is required to neutralize 25.1 mL of a 0.167 M calcium hydroxide solution

Answers

Answer:

46.32 mL

Explanation:

We'll begin by writing the balanced equation for the reaction. This is illustrated below:

2HNO₃ + Ca(OH)₂ —> Ca(NO₃)₂ + 2H₂O

From the balanced equation above,

The following data were obtained:

Mole ratio of the acid, HNO₃ (nA) = 2

Mole ratio of the base, Ca(OH)₂ (nB) = 1

Next, we shall write out the data obtained from the question. This includes:

Molarity of the acid, HNO₃ (Ma) = 0.181 M

Volume of the base, Ca(OH)₂ (Vb) = 25.1 mL

Molarity of the base, Ca(OH)₂ (Mb) = 0.167 M

Volume of the acid, HNO₃ (Va) =?

Finally, we shall determine the volume of the acid, HNO₃ as shown below:

MaVa/ MbVb = nA/nB

0.181 × Va / 0.167 × 25.1 = 2/1

0.181 × Va / 4.1917 = 2

Cross multiply

0.181 × Va = 4.1917 × 2

0.181 × Va = 8.3834

Divide both side by 0.181

Va = 8.3834 / 0.181

Va = 46.32 mL

Therefore, the nitric acid, HNO₃ required for the reaction is 46.32 mL

PLS HURRY
What methods are you using to test this (or each) hypothesis?

Answers

you use a thesis to state your hypothesis and to think what would happen to the experiment

Answer:

Fair test.

PLS GIVE BRAINLIEST

Graphite is sometimes used to reduce the friction between
two surfaces that are rubbing together.
Explain how it does this.

Answers

Because of gravity influence

Graphite is sometimes used to reduce the friction between two surfaces that are rubbing together. Therefore, this happen because of weak covalent bond.

What is graphite?

Graphite is among the most prevalent carbon allotropes. It is also the stable allotrope for carbon, and as such, it is employed in electrochemistry to define the heat of synthesis of carbon compounds. With a hardness of 2.09-2.23 g/cm3, graphite is an excellent conductor of electricity and heat.

Graphite is a large covalent structure in which each carbon atom is covalently linked to three other carbon atoms. Graphite is sometimes used to reduce the friction between two surfaces that are rubbing together. This happen because of weak covalent bond.

Therefore, graphite is sometimes used to reduce the friction between two surfaces that are rubbing together. This happen because of weak covalent bond.

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Ammonia, NH3 is a common base with Kb of 1.8 X 10-5. For a solution of 0.150 M NH3:
Write the equation for the ionization of ammonia in water.


List all species present in the solution AND determine the concentrations of each.





Determine the pH of this solution.

Answers

The concentrations : 0.15 M

pH=11.21

Further explanation

The ionization of ammonia in water :

NH₃+H₂O⇒NH₄OH

NH₃+H₂O⇒NH₄⁺ + OH⁻

The concentrations of all species present in the solution = 0.15 M

Kb=1.8 x 10⁻⁵

M=0.15

[tex]\tt [OH^-]=\sqrt{Kb.M}\\\\(OH^-]=\sqrt{1.8\times 10^{-5}\times 0.15}\\\\(OH^-]=\sqrt{2.7\times 10^{-6}}=1.64\times 10^{-3}[/tex]

[tex]\tt pOH=-log[OH^-]\\\\pOH=3-log~1.64=2.79\\\\pH=14-2.79=11.21[/tex]

Brad pushed a shopping cart directly toward his car at a constant velocity for 6.0 seconds.
During that time, Brad's daughter jogged past him at 2.4 meters per second, and the cart
moved 6.6 meters. What was the cart's velocity?

Answers

Answer:

Watch Naruto that's the answer

Explanation:

sodium hydroxide is extremely soluble in water. a saturated solution contains 678.57 grams of sodium hydroxide 1.00 liter of solution. calculate the molarity of a saturated sodium hydroxide solution.

Answers

Answer:

M = 17 M

Explanation:

Given data:

Mass of sodium hydroxide = 678.57 g

Volume of solution = 1.00 L

Molarity  of solution = ?

Solution:

Molarity is used to describe the concentration of solution. It tells how many moles are dissolve in per litter of solution.

Formula:

Molarity = number of moles of solute / L of solution

Number of moles of sodium hydroxide:

Number of moles = mass/molar mass

Number of moles = 678.57 g /40 g/mol

Number of moles = 17 mol

Molarity:

M =  17 mol/1.00 L

M = 17 mol/L

M = 17 M

find the volume of a gas at standard pressure if its volume at 1.9 atm is 80 ml?

given:
formula:
substitution:
answer:

Answers

Answer:

1.5 × 10² mL

Explanation:

Step 1: Given data

Initial pressure of the gas (P₁): 1.9 atmInitial volume of the gas (V₁): 80 mLFinal pressure of the gas (P₂): 1.0 atm (standard pressure)Final volume of the gas (V₂): ?

Step 2: Calculate the final volume of the gas

For an ideal gas, we can calculate the final volume of the gas using Boyle's law.

P₁ × V₁ = P₂ × V₂

V₂ = P₁ × V₁/P₂

V₂ = 1.9 atm × 80 mL/1.0 atm

V₂ = 1.5 × 10² mL

Since the pressure decreased, the volume of the gas increased.

Which of the following elements can only form single covalent bonds when forming molecular compounds?

a) Nitrogen
b) Hydrogen
c) Carbon
d) Oxygen

Answers

B. Since Hydrogen only has one electron, it can only form a single bond.

Hydrogen can only form single covalent bonds when forming molecular compounds. Therefore, option B is correct.

What is covalent bond?

A covalent bond is a type of chemical bond formed between two or more atoms in which electrons are shared between them. Covalent bonds usually occur between nonmetal atoms and are formed by the sharing of valence electrons.

Hydrogen can only form a single covalent bond because it has only one valence electron and needs one more electron to complete its valence shell, making it stable.

Nitrogen can form triple covalent bonds, carbon can form multiple covalent bonds, and oxygen can form double covalent bonds in molecular compounds.

Thus, option B is correct.

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The internal energy of reaction is -855.1). The reaction has a change of
temperature of 63.20°C that consist of 8.85g of material. Assume the
heat capacity of 2.650J/g °C. What is the work energy of this process..

Answers

The work energy of this process : 2337.298 J

Further explanation  

The laws of thermodynamics 1 state that: energy can be changed but cannot be destroyed or created  

ΔU=Q-W

Q=m.c.Δt

[tex]\tt Q=8.85\times 2.650\times 63.2=1482.198~J[/tex]

the work (W) :

[tex]\tt W=Q-\Delta U\\\\W=1482.198-(-855.1)=2337.298~J[/tex]

Theodor Schwann was a German scientist who wanted to understand how different types of cells worked and performed functions in different tissues. He was one of the first to theorize that all living things are made up of cells.

Rudolf Virchow was a German doctor who wanted to discover the origin of diseases. He accepted the idea that all living things are made up of cells and extended the idea to theorize that many diseases are the result of bacterial cells infecting the body.

The example described above suggests that
A.
scientific discoveries are never made by doctors.
B.
scientists always have the same goals when making related discoveries.
C.
German scientists were the first to disprove cell theory.
D.
people with different goals can make contributions to scientific knowledge.

Answers

D. People with different goals can make contributions to scientific knowledge

Both Schwann and Virchow had different thoughts and ideas. Schwann wanted to understand how cells worked - Virchow wanted to know the origin of diseases. Different goals.

Answer:

D

Explanation:

I got it right on studyisland

A ballon that contains 0.75 l of gad at 25 c is cooled to - 100 c. Calculate the new volume of the baloon

Answers

Answer:

0.44L

Explanation:

Given parameters:

  Initial volume  = 0.75L

  Initial temperature  = 25°C  = 273 + 25 = 298K

  Final temperature  = -100°C  = 273 + (-100) = 173K

Unknown:

New volume of the balloon = ?

Solution:

According to Charles's law;

   "the volume of a fixed mass of a gas varies directly as its absolute temperature if the pressure is constant".

Mathematically;

    [tex]\frac{V_{1} }{T_{1} }[/tex]   =  [tex]\frac{V_{2} }{T_{2} }[/tex]  

  V and T are temperature values

  1 and 2 are the initial and final states

Insert the parameters and solve;

   [tex]\frac{0.75}{298}[/tex]   = [tex]\frac{V_{2} }{173}[/tex]  

    298V₂   = 129.75

           V₂  = 0.44L

What happens to the gravitational potential energy of an object if you bring it higher with respect to the ground? *

Answers

Answer:

Increases

Explanation:

The gravitational potential energy of an object increases as you bring it higher with respect to the ground.

Gravitational potential energy depends on the mass, height and gravity between two bodies;

   Gravitational potential energy  = mgh

m is the mass

g is the height

h is the height

We can clearly see that the higher the elevation, the more the value of the gravitational potential energy.

1. If a solution of sodium chloride has 22.3 g of
NaCl, and a volume of 2.00 L, what is its molarity?

Answers

We are given:

Mass of NaCl in the given solution = 22.3 grams

Volume of the given solution = 2 L

Number of Moles of NaCl:

We know that the number of moles = Given mass / Molar mass

Number of moles = 22.3 / 58.44 = 0.382 moles

Molarity of NaCl in the Given solution:

We know that Molarity of a solution = Moles of Solute / Volume of Solution(in L)

Molarity = 0.382 / 2

Molarity = 0.191 M

Convert 85.02g to mg (1 mg=10^-3g)

Answers

Answer:

85,020 milligrams

Explanation:

Multiply the mass value by 1,000

Considering the patterns you have noticed in this activity, which statement best explains why a compound with the molecular formula CH3 doesn't exist in nature?
A. Hydrogen typically needs four bonds to reach a noble gas configuration.
B. Carbon needs more than just three bonds to reach a noble gas configuration. C. The chemical CH3 does not react with other substances because of its high stability.
D. CH3 has three double bonds, which fails to give it a noble gas configuration​

Answers

Answer:

The answer is B

Explanation:

I had the same question and I chose B and it was correct.

Answer:

B. Carbon needs more than just three bonds to reach a noble gas

Explanation:

PLATO ANSWER

PLATO EXPLANATION-

Each hydrogen atom can make only one bond, but a carbon atom needs four bonds to be stable. Therefore, three hydrogen atoms are not enough for the carbon atom to make four bonds.

PLS HELP!!!
What does it mean when there is a physical change?


A new substance has been formed.


Matter has changed on the molecular level.


Matter has changed from one substance into another.


Matter has changed size, shape or form.

Answers

Answer:

Physical Change. Physical changes are changes in which no bonds are broken or formed. This means that the same types of compounds or elements that were there at the beginning of the change are there at the end of the change.

The enthalpy change of reaction 1 is -114 kJ mol-1
reaction 1
2NaOH(aq) + H2SO4(aq)
→ Na2SO4(aq) + 2H2O(1)
By using this information, what is the most likely value for the enthalpy change of reaction 2?
reaction 2
Ba(OH)2(aq) + 2HCl(aq) → BaCl2(aq) + 2H2O(1)​

Answers

Answer:

-114kJ mol-1

Explanation:

Definition of the enthalpy change of neutralization: the energy released with the formation of 1 mole of water when neutralization takes place between an acid and a base.

Since both reactions yield the same number of moles of water, the answer should be -114kJ mol-1.

The statement for the enthalpy change of reaction 2 is "-114 kJ"

What is enthalpy change?

The change in enthalpy (ΔH) is a quantity of heat of a system. The enthalpy change is the amount of heat that enters or exits a system during a reaction.

One equivalent of hydrogen ions is neutralised with one equivalent of hydroxide ions in the reaction 1,

NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)

The change in enthalpy is given as -114 kJ.

Two equivalents of hydrogen ions are neutralised with two equivalents of hydroxide ions in the reaction 2,

Ba(OH)2 + H2SO4 (aq) → BaSO4 (s) + 2H2O (l)

But, that primary ionic reaction is same for both the reaction in which hydrogen ion combines with hydroxide ion to generate a water molecule. So, the enthalpy change of reaction 1 would be exactly same as for reaction 2.

The neutralization enthalpy comes out to be -114 kJ.

Hence the correct answer is -114 kJ.

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How many milliliters of 2.00 M H2SO4 will react with 28.0 g of NaOH?

Answers

Taking into account the reaction stoichiometry and the definition of molarity, 175 mL of 2 M H₂SO₄ will react with 28.0 g of NaOH.

Reaction stoichiometry

In first place, the balanced reaction is:

H₂SO₄ + 2 NaOH  → Na₂SO₄ + 2 H₂O

By reaction stoichiometry (that is, the relationship between the amount of reagents and products in a chemical reaction), the following amounts of moles of each compound participate in the reaction:

H₂SO₄: 1 moleNaOH: 2 moles  Na₂SO₄: 1 moleH₂O: 2 moles

The molar mass of the compounds is:

H₂SO₄: 98 g/moleNaOH: 40 g/moleNa₂SO₄: 142 g/moleH₂O: 18 g/mole

Then, by reaction stoichiometry, the following mass quantities of each compound participate in the reaction:

H₂SO₄: 1 mole× 98 g/mole= 98 gramsNaOH: 2 moles× 40 g/mole= 80 gramsNa₂SO₄: 1 mole× 142 g/mole= 142 gramsH₂O: 2 moles× 18 g/mole= 36 grams

Definition of molarity

Molar concentration or molarity is a measure of the concentration of a solute in a solution and indicates the number of moles of solute that are dissolved in a given volume.

The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:

[tex]Molarity= \frac{number of moles}{volume}[/tex]

Molarity is expressed in units [tex]\frac{moles}{liter}[/tex].

Moles of H₂SO₄ required

The following rule of three can be applied: If by reaction stoichiometry 80 grams of NaOH react with 1 mole of H₂SO₄, 28 grams of NaOH react with how many moles of H₂SO₄?

[tex]moles of H_{2}S O_{4} =\frac{28 grams of NaOHx1 mole ofH_{2}S O_{4} }{80 grams of NaOH}[/tex]

moles of H₂SO₄= 0.35 moles

Volume of H₂SO₄ required

In this case, you know:

Molarity= 2 M= 2 [tex]\frac{moles}{liter}[/tex]amount of moles= 0.35 moles

Replacing in the definition of molarity:

[tex]2 \frac{moles}{liter}= \frac{0.35 moles}{volume}[/tex]

Solving:

2 [tex]\frac{moles}{liter}[/tex] × volume= 0.35 moles

volume= 0.35 moles ÷ 2 [tex]\frac{moles}{liter}[/tex]

volume= 0.175 liters= 175 mL (being 1 L= 1000 mL)

Finally, 175 mL of 2 M H₂SO₄ will react with 28.0 g of NaOH.

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the reaction stoichiometry:

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molarity:

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Everything in outer space including stars, planets, and galaxies
O A. Solar System
B. Universe
OC. Galaxy
D. Biosphere
I

Answers

Answer:

Universe.

Explanation:

Biosphere is just a planet. Solar system contains planets and star. Galaxy holds multiple solar systems only. Universe hold everything, biospheres, solar systems, and galaxies. I hope this helps :D

Answer:

B.

Explanation:

A solar system is IN a galaxy. Its not A.

A Galaxy doesnt have other galaxies in it. Its not c

A biosphere is only referring to earth. its not D.

Therefore, it is B. A universe is everything in outer space including stars, planets, and galaxies.

When a metal reacts with hydrogen carbon dioxide gas is produced? True or False

Answers

Answer:

false

Explanation:

"When a metal reacts with hydrogen carbon dioxide gas is produced" statement is false.

What is a chemical equation?

A chemical reaction is a representation of symbols of the elements to indicate the amount of substance and moles of reactant and product.

Generally, metals do not react with hydrogen. But some metals like sodium, potassium, calcium and magnesium force the hydrogen atom to accept the electrons given by these elements and form salt-like ionic solid compounds called metal hydrides.

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Alcohol is a
Depressant
Muscle relaxer
Both

Answers

Alcohol is both a Depressant and a Muscle Relaxer. Therefore the answer would be both!

Hope this helps :)

Why is Mg++ smaller than Mg atom?​

Answers

Answer:

The magnesium ion is much smaller than the magnesium atom because magnesium atom contains more electrons as compared to magnesium ion. Explanation: ... Whereas when an atom tends to lose an electron then it acquires a positive charge and size of the atom tends to increase.

Answer:

Because it looses it two electrons to form a stable octet Ionic form..........

Other Questions
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