Solved Examples on Mass Defect
Example 1: A lithium nucleus (Li-7) consists of 3 protons and 4 neutrons. If the mass of a proton is 1.00728 atomic mass units (u) and the mass of a neutron is 1.00867 u, calculate the mass defect of the lithium nucleus.
Solution:
Given:
Number of protons (Z): 3
Number of neutrons (N): 4
Mass of a proton (mp): 1.00728 u
Mass of a neutron (mn): 1.00867 u
Using the formula for mass defect:
Mass Defect = (Z × mp + N × mn) – M
Substituting the given values:
Mass Defect = (3 × 1.00728 + 4 × 1.00867) – 7.036005
Mass Defect = (3.02184 + 4.03468) – 7.036005
Mass Defect = 7.05652 – 7.036005
Mass Defect = 0.020515 u
Example 2: An oxygen nucleus (O-16) contains 8 protons and 8 neutrons. If the mass of a proton is 1.00728 atomic mass units (u) and the mass of a neutron is 1.00867 u, find the mass defect of the oxygen nucleus.
Solution:
Given:
Number of protons (Z): 8
Number of neutrons (N): 8
Mass of a proton (mp): 1.00728 u
Mass of a neutron (mn): 1.00867 u
Using the formula for mass defect:
Mass Defect = (Z × mp + N × mn) – M
Substituting the given values:
Mass Defect = (8 × 1.00728 + 8 × 1.00867) – 15.99491
Mass Defect = (8.05824 + 8.06936) – 15.99491
Mass Defect = 16.12760 – 15.99491
Mass Defect = 0.13269 u
Example 3: A carbon nucleus (C-12) consists of 6 protons and 6 neutrons. If the mass of a proton is 1.00728 atomic mass units (u) and the mass of a neutron is 1.00867 u, calculate the mass defect of the carbon nucleus.
Solution:
Given:
Number of protons (Z): 6
Number of neutrons (N): 6
Mass of a proton (mp): 1.00728 u
Mass of a neutron (mn): 1.00867 u
Using the formula for mass defect:
Mass Defect = (Z × mp + N × mn) – M
Substituting the given values:
Mass Defect = (6 × 1.00728 + 6 × 1.00867) – 12.00000
Mass Defect = (6.04368 + 6.05202) – 12.00000
Mass Defect = 12.09570 – 12.00000
Mass Defect = 0.09570 u
How to Calculate Mass Defect?
Concept of mass defect is crucial in the field of nuclear physics. It helps us comprehend the energy released in nuclear reactions and the stability of atomic nuclei. Mass defect refers to the difference in mass between the individual particles within a nucleus (protons and neutrons) and the mass of the nucleus as a whole.
In this article, we will explore the fundamentals of mass defect, including its definition, formula, derivation, and methods of calculation of mass defect.
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