   Chapter 19, Problem 49E

Chapter
Section
Textbook Problem

# Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are H 1 1 , 1.00782 u; H 1 2 , 2.01410 u; and an electron, 5.4858 × 10−4 u. (Hint: Think carefully about how to account for the electron mass.) H 1 1   +   H 1 1   →   H 1 2   +   e + 1 0

Interpretation Introduction

Interpretation:

The amount of energy released per gram of hydrogen reacted for the given reaction 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.

Explanation

The atomic mass of 11H is 1.0078amu.

The atomic mass of 12His2.01410amu.

The mass of neutron is 1.0087amu.

Number of protons in 12H=1

Number of neutron in 12H=1

The stated reaction is,

11H+11H12H+10e

The mass defect is calculated by the formula,

Δm=[Mass of 12Hnucleus+Massofpositron][2×Massof12Hnucleus]Δm=([(Atomicmass of 12HnucleusMassofelectron)+Massofpositron][2(Atomicmassof11H-massofelectron)])

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

Δm=2.01410[2(1.007825.4858×104)]Δm=0.0044amu/nucleus

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

1amu=1.66×1027Kg

Therefore, the conversion of 0.0044amu/nucleus into kg/nucleus is,

0.0044amu/nucleus=(0.0044×1.66×1027)kg/nucleus=-7.30×10-31Kg/nucleus_

Therefore, the mass defect (Δm) of 12H is -7.30×10-31Kg/nucleus_

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