   Chapter 19, Problem 48E

Chapter
Section
Textbook Problem

# The binding energy per nucleon for magnesium-27 is 1.326 × 10−12 J/nucleon. Calculate the atomic mass of 27Mg.

Interpretation Introduction

Interpretation: The binding energy per nucleon of 27Mg is given. The atomic mass of 27Mg 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 atomic mass of 27Mg .

Explanation

Explanation

The value of ΔE is given to be 1.326×1012J/nucleon .

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 ΔE and C in the equation.

ΔE=Δmc21.326×1012Kgm2s-2nucleon=Δm×(3×108ms1)2Δm=1.326×1012Kgm2s-2nucleon9×1016m2s2Δm=1.4733×1029Kg/nucleon

Conversion of Kg/nucleon to amu/nucleon is done as,

1.66×1027Kg=1amu

Therefore, the conversion of 1.4733×1029Kg/nucleon into amu/nucleon is,

1.4733×1029Kg/nucleon=1.4733×10291.66×1027amu/nucleon=0

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