Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
bartleby

Concept explainers

Question
Book Icon
Chapter 46, Problem 14SP
To determine

The binding energy of carbon-12 (12C with Z=6) whose atomic mass is 12.000000 u.

Expert Solution & Answer
Check Mark

Answer to Problem 14SP

Solution:

92.16 MeV

Explanation of Solution

Given data:

The mass of the carbon atom is 12.000000 u.

The atomic mass number of the carbon atom is 12.

Formula used:

The expression for the atomic mass number of an atom is written as

A=Z+N

Here, Z is the atomic number and N is the number of neutrons.

The expression for the binding energy of the nucleus is written as

BE(ZMH+NMnMA)c2

Here, MH is the mass of hydrogen, Mn is the mass of neutron, MA is the atomic mass, and c is the speed of light.

Explanation:

Recall the expression for the atomic mass number of an atom:

A=Z+N

Rearrange the expression for N

N=AZ

Substitute 12 for A and 6 for Z

N=126=6

This is the number of neutrons present in carbon-12.

Write the expression for the binding energy of carbon-12:

BE(ZMH+NMnMC)c2

Here, MC is the mass of the carbon atom.

Substitute 6 for Z, 6 for N, 1.007825 u for MH, 12.000000 u for MC, and 1.008665 u for MN

BE[6(1.007825 u)+6(1.008665 u)12.000000 u]c2=(0.09894 u)(931.494095 MeVc2)c2=92.16 MeV

Conclusion:

Hence, the binding energy of carbon-12 is 92.16 MeV.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Calculate the binding energy per nucleon of the carbon nucleus, 612?. (Given mass of proton = 1.007276 u, mass of neutron = 1.008665 u, mass of electron = 0.000549 u and mass of Carbon-12 atom = 12.000000 u)
The atomic mass of 14C is 14.003242 u. (a) Can the β- decay of 14C occur spontaneously? Explain. What is the value of the disintegration energy Q? The atomic masses of 14N (Z=7) and of 14B (Z=5) are respectively, 14.003074 u and 14.025404 u. (b) What becomes of this energy Q?
Given the atomic masses below, calculate the exact nuclear binding energy (in MeV to 4 SD) of a N-15 atom.   Neutron = 1.008665 u                                 Hydrogen atom = 1.007825 u Proton   = 1.007276 u                                 Nitrogen-15 atom = 15.000109 u   A.    97.18 MeV   B.    115.5 MeV   C.    94.06MeV   D.    92.25 MeV   E.    108.3 MeV
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
  • Text book image
    Modern Physics
    Physics
    ISBN:9781111794378
    Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
    Publisher:Cengage Learning
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning