Mass difference in physics, often referred to as mass defect, is the difference between the mass of an atomic nucleus and the sum of the masses of its constituent protons and neutrons. This difference arises because some mass is converted into binding energy, which holds the nucleus together.
Understanding Mass Defect
The mass defect (Δm) is calculated by comparing the total mass of individual nucleons (protons and neutrons) to the actual mass of the nucleus. This difference, according to Einstein's famous equation E=mc², is equivalent to the binding energy of the nucleus. The reference provides a formula for calculating mass defect:
Δm = [Z(mp + me) + (A – Z)mn] – matom
Where:
- Δm = mass defect (atomic mass unit, amu)
- mp = mass of a proton (1.007277 amu)
- mn = mass of a neutron (1.008665 amu)
- me = mass of an electron (0.000548597 amu)
- matom = mass of the atom (amu)
- Z = atomic number (number of protons)
- A = mass number (total number of protons and neutrons)
Here's a breakdown of the components of the formula:
- Z(mp + me): This calculates the total mass of all protons and their corresponding electrons in the atom. This portion calculates the mass of the atom’s constituent protons and electrons. Note that for mass defect, you calculate with the atomic mass (including the electrons) rather than the mass of only the nucleus.
- (A – Z)mn: This calculates the total mass of all neutrons in the nucleus. Subtracting the number of protons (Z) from the mass number (A) gives the number of neutrons.
- matom: This is the actual measured mass of the atom. This is the actual mass of a given atom.
Steps to Calculate Mass Difference (Mass Defect)
Here are the steps involved in calculating mass difference:
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Identify the Nucleus: Determine the atomic number (Z) and mass number (A) of the nucleus you're studying. This is needed to identify the number of protons and neutrons.
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Determine the Mass of the Nucleus (matom): Find the experimental atomic mass for the nuclide of interest. You will need to refer to known values from scientific tables or sources.
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Calculate Total Mass of Protons and Electrons: Multiply the atomic number (Z) by the sum of mass of a proton and mass of an electron. This is the mass of all the protons plus their corresponding electrons.
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Calculate Total Mass of Neutrons: Subtract the atomic number (Z) from the mass number (A) to get the number of neutrons, and multiply by the mass of a neutron.
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Apply the Formula: Subtract the actual mass of the nucleus (matom) from the combined mass of individual protons, electrons, and neutrons to get the mass difference.
- Δm = [Z(mp + me) + (A – Z)mn] – matom
Example Calculation
Let's say you want to calculate the mass defect of Helium-4 (⁴₂He).
- Z = 2 (2 protons)
- A = 4 (4 nucleons: 2 protons + 2 neutrons)
- mp = 1.007277 amu
- me = 0.000548597 amu
- mn = 1.008665 amu
- matom = 4.002603 amu (experimental mass of Helium-4)
Calculation:
- Total mass of protons and electrons = 2 * (1.007277 amu + 0.000548597 amu) = 2.015651194 amu
- Total mass of neutrons = (4 - 2) * 1.008665 amu = 2.01733 amu
- Combined mass of nucleons = 2.015651194 amu + 2.01733 amu= 4.032981194 amu
- Mass defect (Δm) = 4.032981194 amu - 4.002603 amu= 0.030378194 amu
Therefore, the mass defect of Helium-4 is 0.030378194 amu.
Significance
The mass defect is a fundamental concept in nuclear physics and demonstrates the principle of mass-energy equivalence. Understanding this concept helps explain why the nucleus is stable and how nuclear reactions release energy.
