menu
bartleby
search
close search
Hit Return to see all results
close solutoin list

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass= 12.0000 u) and uranium-235 (atomic mass= 235.0439 u). The atomic mass of H 1 1 is 1.00782 u and the mass of a neutron is 1.00866 u. The most stable nucleus known is 56 Fe (see Exercise 44). Would the binding energy per nucleon for 56 Fe be larger or smaller than that of 12 C or 235 U? Explain.

BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 45E
Textbook Problem
1387 views

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass= 12.0000 u) and uranium-235 (atomic mass= 235.0439 u). The atomic mass of H 1 1 is 1.00782 u and the mass of a neutron is 1.00866 u. The most stable nucleus known is 56Fe (see Exercise 44). Would the binding energy per nucleon for 56Fe be larger or smaller than that of 12C or 235U? Explain.

Interpretation Introduction

Interpretation: The binding of carbon- 12 and uranium- 235 is to be calculated. Justification of whether the binding energy per nucleon of 56Fe be greater or smaller than that of 12C or 235U is to be stated.

Concept introduction: The sum of masses of the component nucleons and the actual mass of a nucleus is known as the mass defect and it can be used to calculate the nuclear binding energy.

To determine: The binding energy per nucleon of carbon- 12 and uranium- 235 .

Explanation of Solution

Explanation

Given

The atomic mass of 612C is 12.000amu .

Mass of 11H 1.00782amu .

The mass of neutron is 1.00866amu .

Number of protons in 612C=6

Number of neutrons in 612C=6

Mass defect is calculated by the formula,

Δm=Atomicmassof612Cnucleus[Numberofprotons×Massof11HprotonNumberofneutrons×Massofneutron]

Substitute the value of the atomic mass 612C , the number of protons and mass of the 11H proton and that of the neutron in the above equation.

Δm=12.000[(6×1.0078)+(6×1.00866)]Δm=12.0006.04696.05196Δm=12.00012.09888Δm=0.09888amunucleus

The conversion of amu/nucleus to Kg/nucleus is done as,

1amu=1.66×1027Kg

Therefore, the conversion of 0.589amu/nucleus into kg/nucleus is,

0.09888amu/nucleus=(0.09888×1×1.66×1027)kg/nucleus=-0.1641408×10-27Kg/nucleus_

Therefore, the mass defect (Δm) of 612C is -0.1641408×10-27Kg/nucleus_ .

Explanation

The binding energy per nucleon is calculated by Einstein’s mass energy equation, that is,

ΔE=ΔmC2

Where,

  • ΔE is the change in energy.
  • Δm is the change in mass.
  • C is the velocity of light.

Substitute the values of Δm and C in the equation.

ΔE=ΔmC2ΔE=(0.1641408×10-27kgnucleus)(3×108ms)2ΔE=-1.477×10-11J/nucleus_

Therefore, the energy released per nucleus is -1.477×10-11J/nucleus_ .

Explanation

The binding energy per nucleon is calculated by the formula,

Binding energy per nucleon=Bindingenergy per nucleusNumberofprotons+Numberofneutrons

Substitute the value of the binding energy per nucleus, the number of protons and the number of neutrons in the above equation.

Binding energy per nucleon=Bindingenergy per nucleus(Numberofprotons+Numberofneutrons)=1.477×101112J/nucleon=-1.23×10-12J/nucleon_

Explanation

The atomic mass of 92235U 235.0439amu .

Mass of 11H 1.00782 amu .

The mass of neutron is 1.00866amu

Number of protons in 92235U=92

Number of neutrons in 92235U=143

The mass defect of 92235U is calculated by the formula,

Δm=Mass of 92235Unucleus [Numberofprotons×massof11HprotonNumberofneutrons×massofneutron]

Substitute the value of the mass 92235U , the number of protons and mass of the 11H proton and that of the neutron in the above equation.

Δm=235.0439[(92×1.00782)+(143×1.00866)]Δm=235.043992.7194144.2383Δm=1.91388amu/nucleus

The conversion of amu/nucleus to Kg/nucleus is done as,

1amu=1.66×1027Kg

Therefore, the conversion of 0.589amu/nucleus into kg/nucleus is,

1.91388amu/nucleu=(1.9138×1×1.66×1027)kg/nucleus=-3.17704×10-27Kg/nucleus_

The mass defect (Δm) of 92235U is

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 18 Solutions

Chemistry: An Atoms First Approach
Show all chapter solutions
add
Ch. 18 - When nuclei undergo nuclear transformations, rays...Ch. 18 - There is a trend in the United States toward using...Ch. 18 - Which type of radioactive decay has the net effect...Ch. 18 - Consider the following graph of binding energy per...Ch. 18 - What are transuranium elements and how are they...Ch. 18 - Scientists have estimated that the earths crust...Ch. 18 - Why are the observed energy changes for nuclear...Ch. 18 - Natural uranium is mostly nonfissionable 238U; it...Ch. 18 - Much of the research on controlled fusion focuses...Ch. 18 - A recent study concluded that any amount of...Ch. 18 - Write an equation describing the radioactive decay...Ch. 18 - In each of the following radioactive decay...Ch. 18 - Supply the missing particle, and state the type of...Ch. 18 - Write balanced equations for each of the processes...Ch. 18 - Write an equation describing Ute radioactive decay...Ch. 18 - In each of the following radioactive decay...Ch. 18 - Uranium-235 undergoes a series of -particle and,...Ch. 18 - The radioactive isotope 247Bk decays by a series...Ch. 18 - One type of commercial smoke detector contains a...Ch. 18 - Thorium-232 is known to undergo a progressive...Ch. 18 - There are four stable isotopes of iron with mass...Ch. 18 - The only stable isotope of fluorine is...Ch. 18 - In 1994 it was proposed (and eventually accepted)...Ch. 18 - Many elements have been synthesized by bombarding...Ch. 18 - The rate constant for a certain radioactive...Ch. 18 - Americium-241 is widely used in smoke detectors....Ch. 18 - Krypton consists of several radioactive isotopes,...Ch. 18 - Radioactive copper-64 decays with a half-life of...Ch. 18 - A chemist wishing to do an experiment requiring...Ch. 18 - The curie (Ci) is a commonly used unit for...Ch. 18 - The first atomic explosion was detonated in the...Ch. 18 - Iodine-131 is used in the diagnosis and treatment...Ch. 18 - Technetium-99 has been used as a radiographic...Ch. 18 - Phosphorus-32 is a commonly used radioactive...Ch. 18 - The bromine-82 nucleus has a half-life of 1.0 103...Ch. 18 - Fresh rainwater or surface water contains enough...Ch. 18 - A living plant contains approximately the same...Ch. 18 - Assume a constant 14C/12C ratio of 13.6 counts per...Ch. 18 - A rock contains 0.688 mg 206Pb for every 1.000 mg...Ch. 18 - The mass ratios of 40Ar to 40K also can be used to...Ch. 18 - The sun radiates 3.9 1023 J of energy into space...Ch. 18 - The earth receives 1.8 1014 kJ/s of solar energy....Ch. 18 - Many transuranium elements, such as plutonium-232,...Ch. 18 - The most stable nucleus in terms of binding energy...Ch. 18 - Calculate the binding energy in J/nucleon for...Ch. 18 - Calculate the binding energy per nucleon for H12...Ch. 18 - The mass defect for a lithium-6 nucleus is 0.03434...Ch. 18 - The binding energy per nucleon for magnesium-27 is...Ch. 18 - Calculate the amount of energy released per gram...Ch. 18 - The easiest fusion reaction to initiate is...Ch. 18 - The typical response of a Geiger-Mller tube is...Ch. 18 - When using a Geiger-Mller counter to measure...Ch. 18 - Consider the following reaction to produce methyl...Ch. 18 - A chemist studied the reaction mechanism for the...Ch. 18 - Uranium-235 undergoes many different fission...Ch. 18 - Breeder reactors are used to convert the...Ch. 18 - Which do you think would be the greater health...Ch. 18 - Consider the following information: i. The layer...Ch. 18 - Predict whether each of the following nuclides is...Ch. 18 - Each of the following isotopes has been used...Ch. 18 - The mass percent of carbon in a typical human is...Ch. 18 - At a flea market, youve found a very interesting...Ch. 18 - Define third-life in a similar way to half-life,...Ch. 18 - A proposed system for storing nuclear wastes...Ch. 18 - During World War II, tritium (3H) was a component...Ch. 18 - A positron and an electron can annihilate each...Ch. 18 - A small atomic bomb releases energy equivalent to...Ch. 18 - During the research that led to production of the...Ch. 18 - Using the kinetic molecular theory (see Section...Ch. 18 - Consider the following reaction, which can take...Ch. 18 - Photosynthesis in plants can be represented by the...Ch. 18 - Strontium-90 and radon-222 both pose serious...Ch. 18 - Complete the following table with the nuclear...Ch. 18 - A certain radioactive nuclide has a half-life of...Ch. 18 - Iodine-131 has a half-life of 8.0 days. How many...Ch. 18 - Rubidium-87 decays by -particle production to...Ch. 18 - Given the following information: Mass of proton =...Ch. 18 - Which of the following statement(s) is(are) true?...Ch. 18 - Naturally occurring uranium is composed mostly of...Ch. 18 - The curie (Ci) is a commonly used unit for...Ch. 18 - A 0.10-cm3 sample of a solution containing a...Ch. 18 - Zirconium is one of the few metals that retains...Ch. 18 - In addition to the process described in the text,...Ch. 18 - The most significant source of natural radiation...Ch. 18 - To determine the Ksp value of Hg2I2, a chemist...Ch. 18 - Estimate the temperature needed to achieve the...Ch. 18 - A reported synthesis of the transuranium element...Ch. 18 - Radioactive cobalt-60 is used to study defects in...

Additional Science Textbook Solutions

Find more solutions based on key concepts
Show solutions add
A person who wishes to meet nutrient needs while not over consuming calories is wise to master a. the concept o...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What is the fuel density in units of kg/L?

Chemistry & Chemical Reactivity

What is the maximum number of bonds that a carbon atom can form?

Biology: The Dynamic Science (MindTap Course List)

Galileo thought about whether acceleration should be defined as the rate of change of velocity over time or as ...

Physics for Scientists and Engineers, Technology Update (No access codes included)

How do penguins differ from other marine birds?

Oceanography: An Invitation To Marine Science, Loose-leaf Versin