The difference in mass of a nucleus and its constituent nucleons is called the ____________.
Understanding Nuclear Mass Difference: The Mass Defect
When we examine the mass of an atomic nucleus, we find something interesting. The actual mass of a nucleus is always slightly less than the combined mass of its individual protons and neutrons (which are collectively called nucleons) if they were separate.
This difference in mass is a fundamental concept in nuclear physics and is given a specific name. Let's look at the options provided:
- Packing fraction: This is related to the mass defect per nucleon divided by the mass number. It's not the mass difference itself.
- Mass defect: This is defined precisely as the difference between the total mass of the individual constituent nucleons and the actual mass of the nucleus.
- Binding energy: This is the energy equivalent of the mass defect according to Einstein's famous equation, \(E = mc^2\). While related, it is energy, not mass difference.
- Binding energy per nucleon: This is the binding energy divided by the number of nucleons in the nucleus.
Let's delve deeper into the definition of Mass Defect.
Defining Mass Defect
Consider a nucleus with Z protons and N neutrons. The total number of nucleons is A = Z + N.
The total mass of the individual nucleons if they were separate would be:
\(m_{\text{expected}} = Z \cdot m_p + N \cdot m_n\)
where \(m_p\) is the mass of a proton and \(m_n\) is the mass of a neutron.
The actual measured mass of the nucleus is \(M_{\text{nucleus}}\).
The Mass Defect, denoted by \(\Delta m\), is the difference between the expected mass and the actual nucleus mass:
\(\Delta m = m_{\text{expected}} - M_{\text{nucleus}}\)
So, \(\Delta m = (Z \cdot m_p + N \cdot m_n) - M_{\text{nucleus}}\)
This difference, the mass defect, accounts for the mass that is converted into energy to hold the nucleons together in the nucleus. This energy is known as the binding energy.
Therefore, the difference in mass of a nucleus and its constituent nucleons is called the Mass defect.
| Term | Definition | Relationship to Mass Difference |
|---|---|---|
| Mass Defect | Difference between the total mass of individual nucleons and the actual mass of the nucleus. | This *is* the mass difference asked about in the question. |
| Binding Energy | Energy equivalent of the mass defect (\(\Delta m c^2\)). The energy needed to break a nucleus into its constituent nucleons. | Related via \(E = mc^2\), but is energy, not mass. |
| Packing Fraction | \(( \Delta m / A ) / m_{amu}\) (where \(m_{amu}\) is atomic mass unit). Related to mass defect per nucleon relative to atomic mass unit. | Derived from mass defect, but not the mass difference itself. |
| Binding Energy per Nucleon | Binding energy divided by the number of nucleons (A). | Derived from binding energy, not the mass difference itself. |
Based on the definitions, the term that specifically describes the difference in mass between a nucleus and its constituent nucleons is the Mass defect.
Revision Table: Nuclear Mass Concepts
| Concept | Formula/Description |
|---|---|
| Nucleus | The central part of an atom, containing protons and neutrons. |
| Nucleons | Protons and neutrons found in the nucleus. |
| Mass Defect (\(\Delta m\)) | \((Z \cdot m_p + N \cdot m_n) - M_{\text{nucleus}}\) |
| Binding Energy (BE) | \(\Delta m \cdot c^2\) |
| Binding Energy per Nucleon (BE/A) | \(\text{BE} / A\) |
| Packing Fraction (f) | \(f = (\Delta m / A) / m_{amu}\) or \(f = (M - A) / A\) where M is isotopic mass and A is mass number. |
Additional Information: Why Mass is Lost
The reason the nucleus's mass is less than the sum of its parts is explained by Einstein's principle of mass-energy equivalence, \(E = mc^2\). When protons and neutrons bind together to form a nucleus, a significant amount of energy is released. This energy is the binding energy that holds the nucleus together.
According to \(E = mc^2\), if energy is released, there must be a corresponding decrease in mass. This lost mass is the mass defect. Conversely, to break a nucleus apart into its individual protons and neutrons, this same amount of energy (the binding energy) must be supplied.
The stability of a nucleus is related to its binding energy per nucleon. Nuclei with higher binding energy per nucleon are generally more stable.
Important Questions from Nucleus
- The binding energy B of a nucleus is approximated by the formula B = a 1 A − a 2 A 2/3 − a 3 Z 2 A −1/3 − a 4 (A − 2Z) 2 A −1 where Z is the atomic number and A is the mass number of the nucleus. If \(\rm\frac{a_4}{a_3}\) ≃ 30, the atomic number Z for naturally stable isobars (constant value of A) is
What are the main constituents of biogas?
The energy equivalent of mass associated with the rest mass of an electron, is nearly:
- Considering that the radius of an atomic nucleus, $R$, can be approximated by the formula $R = R_0 A^{1/3}$, where $R_0 \approx 1.2 \times 10^{-15}$ m is the Fermi radius constant and $A$ is the mass number, and the average mass of a single nucleon is approximately $1.67 \times 10^{-27}$ kg. Calculate the approximate order of magnitude of nuclear matter density in $\text{kg/m}^3$.
- The mass number of argon is 40. Which one of the following statements is correct?
