For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined. Concept Introduction: Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy This quantity represents the conversion of mass to energy occurs during an exothermic reaction. Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, Δ E = ( Δ m ) c 2 Where, ( Δ m ) is called mass defect. The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

Question

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Answer 1

Question

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

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Answer 2

Question

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

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Answer 3

Question

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Answer 6

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Answer 7

Chapter 19, Problem 19.76QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

Answer 8

(a)

Expert Solution

Answer to Problem 19.76QP

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In case of $Sr90$ decay, the mass defect is

$Δm=(massY90+mass e-)-massSr90$

Chemistry, Chapter 19, Problem 19.76QP

$=(-)3.7430× 10-5 amu)×1g6.022×1023amu =6.216 10-29 g =-6.216×10-32kg$

The energy change is given by :

$ΔE(Δm)c2$

$(-6.216×10-32kg)(3.00×108m/s)2$

$=5.59×10-15kgm2/s2=5.59×10-15J$

Similarly for $Y90$ decay, we have

$Δm=(massZr90+masse-)-massY90$

$[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu$

$(-1.9004 ×10−3 amu)×1 g6.022×1023 amu=−3.156× 10−27g$

= $- 3.156× 10−30kg$

And the energy change is given by:

$ΔE=$ $(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J$

The energy released in the above two decays is $5.59×10-15 J and 2.84×10-13J.$

The total amount of energy released is:

$(5.59×10-15 J)+2.84×10-13J=2.90×10-13J$

Answer 13

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Answer 14

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles $90Sr$ decaying in a year.

Answer 15

(b)

Expert Solution

Answer to Problem 19.76QP

The number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

$k = 0.693t1/2=0.69328.1yr=0.0247 yr-1$

To calculate the number of moles $90Sr$ decaying in a year, we apply the following equation:

$ln NtN0=-kt$

$lnx1=-(0.0247yr-1)(1yr)$

Where x is the number of moles nuclei left over .solving, we obtained the value of x

$x = 0.9756 mol 90Sr$

Thus the number of moles of nuclei which decay in a year is :

$(1- 0.9756) mol = 0.0244 mol$

This is a reasonable number since it takes 28.1 years for 0.5 moles of $90Sr$ to decay

Answer 20

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Answer 21

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy

This quantity represents the conversion of mass to energy occurs during an exothermic reaction.

Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is, $ΔE = (Δm) c2$

Where, $(Δm)$ is called mass defect.

The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of $90Sr$ waste in a year.

Answer 22

(c)

Expert Solution

Answer to Problem 19.76QP

The heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

The half –life of $Y90$ is much shorter than that of $90Sr$ .

We can assume that $Y90$ formed from $90Sr$ and will be converted to $Z90$ .

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

$0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei$

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of $90Sr$ waste in a year is given by:

$heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ$

Answer 27

Ch. 19.1 - Prob. 1PE Ch. 19.1 - Prob. 1RC Ch. 19.2 - Prob. 1RC Ch. 19.2 - Prob. 2PE Ch. 19.2 - What is the change in mass (in kg) for the...Ch. 19.3 - Prob. 1RC Ch. 19.4 - Write a balanced equation for 46106Pd(,p)47109Ag.Ch. 19.5 - Prob. 1RC Ch. 19 - Prob. 19.1QP Ch. 19 - Prob. 19.2QP

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Answer to Problem 19.76QP

Explanation of Solution

Answer to Problem 19.76QP

Explanation of Solution

Answer to Problem 19.76QP

Explanation of Solution

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