# 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

### Chemistry: An Atoms First Approach

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

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 49E
Textbook Problem
194 views

## 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.

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

### Explanation of Solution

Explanation

The atomic mass of 11H is 1.0078amu .

The atomic mass of 12H is 2.01410amu .

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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