Liquid Drop Model in Nuclear Physics
The aim is to explain nuclei's masses and binding energies. The Liquid Drop Model is named after the fact that nuclei are thought to behave similarly to liquids (at least to first order). A liquid's molecules are kept together by the Van der Waals force, which exists only between close neighbours.
Liquid Drop Model of the Nucleus
The liquid drop model of the nucleus explains forces in atomic nuclei as if they were created by a tiny liquid drop in nuclear physics. On a nuclear scale, however, the fluid is made up of nucleons (protons and neutrons). The liquid drop model accounts for the fact that the forces acting on nucleons on the surface vary from those acting on nucleons on the inside, where they are absolutely surrounded by attracting nucleons. This is analogous to considering surface tension as a factor in calculating the energy of a tiny liquid drop.
Key Facts of Nuclear Liquid Drop Model
Nuclei seem to have a constant density, according to scattering studies.
Nuclei have their own volume and surface, where various forces work.
The nucleus is spherical in its ground state.
This spherical nucleus can be twisted into a dumbbell shape and then broken into two fragments if enough kinetic or binding energy is applied.
For the binding energy of nuclei, the Weizsaecker formula is an empirically refined variant of the liquid drop model. The terms are as follows:
Volume term
Surface term
Asymmetry term
Pairing term
Coulomb term.
Binding energies and masses of atomic nuclei can be calculated using the Weizsaecker formula. As a result, we can calculate the energy released per fission.
Semi-Empirical Formula
The von Weizsäcker mass formula (also known as the semi-empirical mass formula – SEMF) was published in 1935 by German physicist Carl Friedrich von Weizsäcker and was one of the first models that could accurately explain the action of nuclear binding energies and thus nuclear masses. The liquid drop model proposed by George Gamow is the basis for this theory.
The atomic nucleus, according to this model, behaves like the molecules in a drop of liquid. The fluid, on the other hand, is made up of nucleons (protons and neutrons) held together by a strong nuclear force. The nucleus' liquid drop model takes into account the fact that nuclear forces on nucleons on the surface vary from those on nucleons in the nucleus' interior. Other attracting nucleons completely surround the interior nucleons. The forces that shape a drop of liquid can be compared to this.
The nucleus is spherical in its ground state. This spherical nucleus can be distorted into a dumbbell shape and then broken into two fragments if enough kinetic or binding energy is applied. The splitting of such heavy nuclei must be followed by energy release since these fragments have a more stable configuration. This model does not account for all of the atomic nucleus’s properties, but it does account for the expected nuclear binding energies.
The Liquid Drop Model
George Gamow suggested the liquid drop model, which was further developed by Niels Bohr and John Archibald Wheeler. It treats the nucleus as an incompressible fluid drop with a very high density that is kept together by the nuclear force (a residual effect of the strong force), with a structure that resembles that of a spherical liquid drop. The liquid drop model, though crude, accounts for most nuclei's spherical shape and allows a rough prediction of binding energy.
The mass formula is solely determined in terms of the number of protons and neutrons it includes. Five terms are described in the original Weizsäcker formula:
Interior nucleon has a certain number of other nucleons in contact with it when an arrangement of nucleons of the same size is packed together into the smallest volume. As a result, the amount of nuclear energy emitted is proportional to the volume.
The presumption that each nucleon interacts with the same number of other nucleons is corrected by surface energy. Since this definition is negative and proportional to the surface area, it is approximately equal to liquid surface tension.
The potential energy of each pair of protons is known as Coulomb energy. The binding energy is diminished since this is a repulsive force.
The Pauli exclusion theory is explained by asymmetry energy (also known as Pauli Energy). Uneven numbers of neutrons and protons mean that one form of the particle will fill higher energy levels while the other will leave lower energy levels empty.
The propensity for proton and neutron pairs to form is explained by pairing energy. Due to spin coupling, an even number of particles is more stable than an odd number.
What are the major achievements of the liquid-drop model?
The liquid-drop model was an efficient model that helped scientists study atomic nuclei. The major achievements of the liquid-drop model are:
It helps in predicting the atomic mass of the nuclei accurately.
It helps in predicting the binding energies of various nuclei accurately.
It helps scientists in predicting the emission of alpha particles and beta particles in radioactivity.
It also efficiently explains the basic features of the process of fission.
What properties can be studied using a liquid-drop model?
The liquid-drop model can be efficiently used to study various properties of nuclear physics. This model considers the nucleus of an atom as a liquid. Nuclear properties, like binding energy, are studied through a liquid-drop model and are expressed in parameters that are associated with a liquid such as a volume energy, compressibility, and surface energy. The model was also used to explain how a nucleus performs when it undergoes fission.
What are the major advantages of the liquid-drop model?
The liquid-drop model has various advantages in the field of nuclear physics. The major advantages of the liquid-drop model are:
The liquid-drop model explains the spherical shape and stability of nuclei very well.
The model helps in predicting the binding energy of the nucleus and also helps us to know how much energy is available for consumption purposes.
The model helps in explaining the radioactive phenomenon of artificial radioactivity and nuclear fission.
Some terminologies related to nuclear physics
Nucleon: it refers to a proton or a neutron in the nucleus of an atom.
Atomic number: it refers to the number of protons present in a nucleus and is denoted as Z.
Atomic mass number: it refers to the number of nucleons present in a nucleus and is denoted as A =N+Z.
Nuclide: it is the term given to a nucleus that contains a specific value of A and Z. the values of A and Z are written next to the chemical symbol in the form of subscript and superscript. The atomic mass number is written in the superscript and the atomic number is written in the subscript.
Isotope: it refers to a nucleus that has the same atomic number but a different atomic mass number. The isotopes generally have similar chemical and atomic behavior but may possess different nuclear properties.
Isotone: it refers to a nucleus that contains a different number of protons but the same number of neutrons.
Isobar: these are just the opposite of isotopes and refer to a nucleus that has the same atomic mass number but a different atomic number.
Mirror nuclei: these refer to a pair of unique nuclei wherein the number of protons in one nucleus, say A is equal to the number of neutrons in the other nuclei, say B, and the number of neutrons in A is equal to the number of protons in B.
Learn more about the liquid drop model of the atomic nucleus by Vedantu from the top subject matter experts and build a strong foundation of nuclear physics. Find out deeper insights into this topic and proceed with better concepts to study advanced subjects.
FAQs on Liquid - Drop Model
1. What is the liquid drop model in nuclear physics?
The liquid drop model is a theory in nuclear physics that treats the atomic nucleus as an incompressible drop of liquid. Proposed by George Gamow, it helps explain nuclear properties like binding energy and the process of nuclear fission by drawing analogies between the forces holding nucleons (protons and neutrons) together and the surface tension forces in a liquid drop.
2. Who were the key scientists behind the liquid drop model?
The initial concept of the liquid drop model was proposed by George Gamow. The model was later developed and refined by Niels Bohr and John Archibald Wheeler, who used it to explain nuclear fission. Additionally, German physicist Carl Friedrich von Weizsäcker developed the semi-empirical mass formula (SEMF) based on this model to accurately calculate the binding energies of atomic nuclei.
3. What are the fundamental assumptions of the liquid drop model?
The liquid drop model is based on several key assumptions:
- The nucleus is treated as a sphere of incompressible matter, meaning its density is constant and independent of its size.
- The nuclear force is identical for every nucleon and acts only over a very short range, similar to intermolecular forces.
- The nuclear force saturates, meaning a nucleon only interacts with its immediate neighbours.
- In its ground state, the nucleus is perfectly spherical due to symmetrical nuclear forces.
4. What are the main achievements of the liquid drop model?
The liquid drop model has several major achievements in nuclear physics:
- It provides an accurate prediction of the atomic mass and binding energy for most nuclei.
- It successfully explains the spherical shape of most nuclei.
- It offers a clear qualitative explanation for the process of nuclear fission.
- It helps in understanding the emission of alpha and beta particles during radioactive decay.
5. How does the liquid drop model explain the process of nuclear fission?
The liquid drop model explains nuclear fission by visualising the nucleus as a liquid drop that can oscillate. When a heavy nucleus, like Uranium-235, absorbs a neutron, it gains excitation energy. This energy causes the spherical 'drop' to vibrate and deform into a dumbbell shape. The electrostatic repulsion between the protons in the two ends of the dumbbell then overcomes the nuclear force, causing the nucleus to split into two smaller, more stable daughter nuclei, releasing a large amount of energy.
6. Why is an atomic nucleus compared to a drop of liquid? What are the key analogies?
An atomic nucleus is compared to a liquid drop because of several striking similarities in their behaviour and properties:
- Constant Density: Both a liquid drop and a nucleus have a density that is largely independent of their size.
- Surface Tension: The strong nuclear force that holds nucleons together acts like the surface tension in a liquid, pulling the nucleus into a spherical shape to minimise surface area.
- Binding Energy: The constant binding energy per nucleon is analogous to the latent heat of vaporization in a liquid, which is the energy required to remove a molecule.
- Energy Excitation: The energy of a nucleus corresponds to the internal thermal vibrations of molecules in a drop.
7. How do the different terms in the semi-empirical mass formula relate to the liquid drop model?
The semi-empirical mass formula (SEMF), or Weizsäcker formula, quantifies the binding energy based on the liquid drop model. Each term represents a physical property of the nuclear 'liquid':
- Volume Term: Represents the energy from nucleons being tightly packed, proportional to the total number of nucleons (A).
- Surface Term: Corrects for the fact that nucleons on the surface have fewer neighbours, reducing the binding energy, analogous to surface tension.
- Coulomb Term: Accounts for the electrostatic repulsion between protons, which also reduces binding energy.
- Asymmetry Term: A quantum mechanical correction favouring an equal number of protons and neutrons.
- Pairing Term: Accounts for the tendency of nucleons to form pairs, adding stability.
8. What are the significant limitations of the liquid drop model that led to other models?
While successful, the liquid drop model fails to explain several key nuclear phenomena, which led to the development of the nuclear shell model. Its main limitations include:
- It cannot explain the extra stability of nuclei with specific numbers of protons or neutrons, known as magic numbers (2, 8, 20, 28, 50, 82, 126).
- It fails to predict the measured spin and magnetic moments of many nuclei.
- It does not accurately account for the low-lying excited energy states observed in most nuclei.
9. Why does the liquid drop model include a 'surface energy' term, and what does it represent?
The surface energy term is included to correct the assumption that every nucleon interacts with the same number of neighbours. Nucleons on the surface of the nucleus are surrounded by fewer nucleons than those in the interior. This results in weaker binding for surface nucleons, reducing the total binding energy of the nucleus. This effect is analogous to surface tension in a liquid, which arises because molecules at the surface experience a net inward force. This term is negative and proportional to the surface area of the nucleus.
