   Chapter 19, Problem 46E

Chapter
Section
Textbook Problem

# Calculate the binding energy per nucleon for H 1 2 and H 1 3 . The atomic masses are H 1 2 , 2.01410 u; and H 1 3 , 3.01605 u.

Interpretation Introduction

Interpretation: The binding energy per nucleon of 12H and 13H is to be calculated.

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 12H and 13H .

Explanation

Explanation

The atomic mass of 11H=1.0078amu

The mass of a neutron is 1.0087amu .

Mass of 12H=2.01410amu

Number of protons in 12H=1

Number of neutrons in 12H=1

The mass defect is calculated by the formula,

Δm=Atomicmass of 12H[Numberofprotons×massof11HprotonNumberofneutrons×massofneutron]

Substitute the value of the atomic mass 12H , the number of protons and mass of the 11H proton and that of the neutron in the above equation.

Δm=2.01410[(1×1.00782)+(1×1.00866)]Δm=2.38×103amu/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,

2.38×103amu/nucleus=(2.38×103×1.66×1027)kg/nucleus=-3.9508×10-30Kg/nucleus_

Therefore, the mass defect (Δm) of 12H is -3.9508×10-30Kg/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=(3.9508×1030)(3×108)2ΔE=35.55×1014J/nucleus

Therefore, the energy released per nucleus is 35.55×1014J/nucleus .

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)=35.55×10142J/nucleon=17.78×10-14J/nucleon_

Explanation

The atomic mass of 11H=1

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