nuclaer rection
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This document discusses nuclear reactions, including: - Nuclear reactions involve changing the composition or energy of an atom's nucleus through bombardment. - Nuclear reactions are represented by equations that balance protons, neutrons, and energy, similar to chemical equations. - The nucleus is made up of protons and neutrons held together by nuclear force; it can be modeled as shells like electrons. - Nuclear reactions obey conservation laws like charge, baryon number, and lepton number.
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5) Other concepts like mass defect, binding energy, and mass-energy equation which are important for understanding nuclear processes.
Nuclear Structure
In 1909, Rutherford performed the Gold Foil Experiment and suggested the following characteristics of the atom:
It consists of a small core, or nucleus, that contains most of the mass of the atom
This nucleus is made up of particles called protons, which have a positive charge
The protons are surrounded by negatively charged electrons, but most of the atom is actually empty space.
In 1913, Bohor proposed the Atomic Model, which suggests that electrons travel around the nucleus of an atom in orbits or definite paths.
Atom consists of a tiny nucleus.
Each orbit has fixed energy that is quantatized.
The energy is emitted or absorb only when an electron jumps from one orbit to another.
Electron can revolve in orbits of fixed angular momentum mvr.
Liquid Drop Model
The nuclei of all elements are considered to be behave like a liquid drop of incompressible liquid of very high density.
In an equilibrium state the nuclei of atoms remain spherically symmetric under the action of strong attractive nuclear forces just like the drop of a liquid which is spherical due to surface tension.
The density of a nucleus is independent of its
size just like the density of liquid which is also
independent of its size.
The protons and neutrons of the nucleus move about
within a spherical enclosure called the nuclear
potential barrier just like the movement of the
molecules of a liquid within a spherical drop of liquid.
. The binding energy per nucleon of a nucleus is constant
Binding Energy
The binding energy, BE, of a nucleus is a measure of the strong force and represents the energy required to separate the nucleus into its constituents protons and neutrons;
Greater the binding energy, the more stable the nucleus.
Volume
The volume of the nucleus is directly proportional to the total number of nucleons present in it.
Density
The density of the nucleus is nearly constant.
Atomic and nuclear physics
Atomic and nuclear physics are related but distinct fields that describe the structure and behavior of atoms and their nuclei. Atomic physics deals with atoms as systems of electrons and an atomic nucleus, while nuclear physics focuses on the nucleus as a system of nucleons (protons and neutrons). A knowledge of these fields is important for nuclear engineers working with nuclear reactors. The document then provides details on the key topics in atomic and nuclear physics, including fundamental particles, atomic and nuclear structure, mass and energy, radiation, nuclear stability, radioactive decay, and nuclear reactions.
Class 12 physics chapter 13 NCERT solutions pdf
Introduction to Class 12 Physics - Nuclei:
In the realm of physics, the study of atomic nuclei constitutes a pivotal and intriguing segment, forming the nucleus of Class 12 Physics. Delving into the heart of matter, this section unravels the intricacies of the atomic nucleus, where protons and neutrons converge to define the essence of elements. From the formidable forces that bind these particles to the dynamic processes of radioactive decay, Class 12 Physics - Nuclei unveils the mysteries that govern the core of our physical reality.
As students embark on this journey, they will explore the minuscule dimensions of the nucleus, grapple with the potent forces that operate within, and unravel the applications that extend from nuclear power generation to medical diagnostics. The study of nuclei encapsulates the very essence of matter and energy, offering profound insights into the fundamental nature of the universe.
Through an exploration of nuclear reactions, radioactivity, and the applications that span from energy production to medical advancements, Class 12 Physics - Nuclei equips students with a comprehensive understanding of the microscopic world that shapes the macroscopic reality we inhabit. The journey into the heart of the atom awaits, promising a voyage into the fundamental building blocks that define the physical universe.
For more updates, visit- www.vavaclasses.com
7.2
1) Nuclear fusion and fission reactions can release large amounts of energy. Fusion occurs when light nuclei join together, as in the Sun, while fission occurs when heavy nuclei split apart.
2) A graph of binding energy per nucleon shows that mid-sized nuclei are most stable, and that both fission and fusion reactions produce fragments with higher binding energy, releasing energy.
3) Nuclear fission in uranium can be triggered by neutrons and produce a chain reaction releasing many neutrons, as used in nuclear weapons and controlled in nuclear power plants. Nuclear fusion is even more powerful but requires extremely high temperatures and pressures to overcome repulsion between positively charged nuclei.
Radioactive_Decay.pptx
1. Radioactive decay occurs through three main types: alpha, beta, and gamma decay. Alpha decay involves emitting an alpha particle, beta decay changes the nucleus via electron or positron emission, and gamma decay releases energy without changing the nucleus.
2. Nuclear reactions can be classified as fission or fusion. Fission occurs when heavy nuclei split into lighter ones and releases energy. Fusion combines light nuclei into heavier ones and also releases energy. These reactions are accompanied by changes in mass and binding energy.
3. Atoms are made of protons, neutrons, and electrons. The Standard Model describes all fundamental particles and their interactions via exchange particles like photons. Quarks combine to form hadrons like protons and
Chapter 21
1) The nucleus is comprised of protons and neutrons, with the number of protons defining the element. 2) Isotopes of the same element have different numbers of neutrons, resulting in slightly different masses. 3) Some nuclei are unstable and undergo radioactive decay through processes like alpha, beta, or gamma emission to become more stable nuclides. 4) Nuclear reactions involve tremendous amounts of energy due to mass-energy equivalence, and can be harnessed through fission in reactors or potential fusion.
Unit i
The atomic mass unit (amu) is used to measure mass in nuclear physics and equals 1.66x10-24 kg. It is used to calculate mass loss and nuclear binding energy. Thomson's plum pudding model depicted atoms as a uniform positively charged sphere with electrons embedded in it. Nuclear binding energy is the energy released when nucleons combine to form an atomic nucleus. Mass defect is the decrease in total mass when particles combine due to their interaction energy. Natural radioactivity comes from isotopes on Earth since its formation, while artificial radioactivity is caused by cosmic rays from the sun. Rutherford scattering refers to alpha particles being repelled by the positive charge concentrated in an atomic nucleus. The atomic number is the number of protons
The chemical components of a
This document discusses the chemical components that make up cells. It begins by explaining that all matter is made up of combinations of elements, which are substances like carbon and hydrogen that cannot be broken down further. Atoms are the smallest particles of elements that retain chemical properties, and molecules are formed by atoms linking together through chemical bonds. The document then discusses the basic structure of atoms, including protons, neutrons, and electrons. It explains that the outermost electrons determine how atoms interact and form different types of chemical bonds, such as ionic bonds formed by electron transfer and covalent bonds formed by electron sharing. These bonds link atoms together into molecules that make up living cells and organisms.
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1. The document discusses analytic functions of complex variables through examples. It defines analytic functions as those whose derivatives of all orders exist in the region of analyticity.
2. The Cauchy-Riemann equations are derived and their implications are explored, including that they imply the Laplace equation and orthogonality of level curves.
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lec33.ppt
The Cauchy Riemann (CR) conditions provide a necessary and sufficient condition for a function f(z) = u(x, y) + iv(x, y) to be analytic in a region. The CR conditions require that the partial derivatives of u and v satisfy ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x. If a function satisfies these conditions at all points in a region, then it is analytic in that region. The document proves this using cases where ∆y = 0 and ∆x = 0, showing the derivatives must be equal. Examples are provided to demonstrate checking functions for analytic
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Complex numbers allow solutions to equations like x2 + 1 = 0 by extending real numbers to include imaginary numbers. A complex number z is defined as z = x + iy, where x and y are real numbers and i is the imaginary unit equal to √-1. Complex numbers can be added and multiplied following specific rules, such as z1 + z2 = (x1 + x2) + i(y1 + y2) for addition and z1z2 = (x1x2 - y1y2) + i(y1x2 + x1y2) for multiplication. The inverse of a complex number z is calculated as z-1 = (x/(x2+y
lec32.ppt
The document discusses properties of complex numbers including:
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1) The document discusses examples of calculating the Jacobian of transformations. It defines the Jacobian as the determinant of the partial derivatives of the transformed coordinates.
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lec41.ppt
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1) The mapping w = ez maps a vertical line in the z-plane to a circle in the w-plane, with the phase angle increasing along the circle.
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lec39.ppt
The document discusses Taylor and Laurent series expansions. It provides examples of using these expansions to represent functions around points.
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2) Several examples are provided of using residues and Jordan's lemma to evaluate definite integrals over the real line or infinite intervals that involve functions with poles, including integrals of x^2, sin(x)/x, 1/(x^2+a^2)^2, and sin(x)/(x(x^2+a^2)).
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lec37.ppt
1) The document discusses evaluating contour integrals using the residue theorem. It provides examples of calculating residues and evaluating integrals where the contour encloses poles.
2) The residue of a function f(z) at a pole z=a is the coefficient of the (z-a)^-1 term in the Laurent series expansion of f(z) about z=a.
3) According to the residue theorem, the value of a contour integral of a function along a closed loop is equal to 2πi times the sum of the residues of the function enclosed by the contour.
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1) The document discusses representation of the Dirac delta function in cylindrical and spherical coordinate systems. It shows that δ(r - r') = δ(ρ - ρ')δ(φ - φ')δ(z - z')/ρ in cylindrical coordinates and δ(r - r') = δ(r - r')δ(θ - θ')δ(φ - φ')/r^2 in spherical coordinates.
2) It also derives the important relation ∇^2(1/r) = -4πδ(r) and shows its application to the Laplace equation for electrostatic potential.
3) The completeness of eigenfunctions of harmonic oscillators and Legend
lec21.ppt
1. The Dirac delta function is an important concept in quantum mechanics and electrodynamics that describes an impulse or large force acting over a very short time interval.
2. The key properties of the Dirac delta function are that it is equal to infinity at a single point and zero everywhere else, and that the integral of the function over its entire range is equal to one.
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lec20.ppt
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lec19.ppt
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lec18.ppt
This document discusses solving a mass-spring system as an eigenvalue problem. It:
1) Sets up differential equations to model the displacements of two masses connected by springs.
2) Transforms the coupled differential equations into a matrix eigenvalue equation.
3) Solves the eigenvalue equation to obtain the frequencies of oscillation for the two masses.
4) Combines the eigenvectors with complex exponential functions to obtain general solutions for the displacements of each mass over time.
lec17.ppt
This document discusses linear transformations and matrices. It introduces how linear transformations on physical quantities are usually described by matrices, where a column vector u representing a physical quantity is transformed into another column vector Au by a transformation matrix A. As an example, it discusses orthogonal transformations, where the transformation matrix A is orthogonal. It proves that for an orthogonal transformation, the inner product of two vectors remains invariant. It also discusses properties of other types of matrices like Hermitian, skew-Hermitian and unitary matrices.
lec16.ppt
This document discusses properties of symmetric, skew-symmetric, and orthogonal matrices. It defines each type of matrix and provides examples. Key points include:
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1) The document discusses calculating the moment of inertia tensor for a cylinder with radius R and height H. It is shown that the only non-zero components of the inertia tensor are Ixx = (3MH + 4MR2)/12, Iyy = Ixx, and Izz = MR2/2.
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lec28.ppt
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lec27.ppt
1) The document discusses tensors with multiple indices and the cross product of two vectors A and B. The components of the cross product vector C are given by Ai Bj - Aj Bi.
2) It describes how tensor components transform between coordinate systems using transformations of partial derivatives. The transformation property for cross products is derived.
3) Tensors are defined by their rank, with the number of covariant and contravariant indices specifying a tensor's rank. Vectors have a rank of 1. Examples calculate tensor components in different coordinate systems.
lec26.ppt
1) There are two types of vectors - contravariant vectors whose components transform according to Equation 1, and covariant vectors whose components transform according to Equation 2.
2) The dot product of two contravariant or two covariant vectors is not independent of the coordinate system.
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nuclaer rection
- 1. WEL COME
- 5. Nuclear reaction is that process in which on bombarding the projectile particle on a nuclear target, a change is produced in composition (i.e. nucleons) of the nucleus. In this process there is change in energy of nucleus also due to which some energy is absorbed or emitted in the nuclear reaction
- 6. Nuclear Equations The two subatomic particles that occur in the nucleus, the proton and the neutron, are called nucleons. The number of protons is the atomic number which determines the identity of the element. The number of protons and neutrons determines the atomic mass of the element. Different isotopes of an element have the same atomic number (same number of protons) but different atomic masses (different number of neutrons)
- 7. The three isotopes of hydrogen have the same number of protons but different numbers of neutrons. Hydrogen-1 is the most common isotope. Hydrogen-2, with an additional neutron, is named deuterium, and hydrogen-3 is called tritium. Neutrons and protons are called nucleons because they are in the nucleus.
- 8. Just like any other chemical reaction, we use symbols to show a nuclear reaction As an example, when uranium 238 emits an alpha particle, it loses 2 protons and 2 neutrons. Nuclear reactions must balance just like any other chemical reaction, but we must also be aware of balancing protons and neutrons HeThU 4 2 234 90 238 92
- 9. The Nature of the Nucleus. Protons and neutrons are held together by a nuclear force when they are very close together. The shell model of the nucleus visualizes the protons and neutrons moving on energy levels or shells, much like the electrons move in shells.
- 10. When separate protons and neutrons come together in a nucleus, energy is released. The more energy that is released, the lower the energy of the final nucleus. The energy of the nucleus depends on the mass and atomic number.
- 11. A nuclear reaction is any process that changes the nucleus of an atom. Radioactive decay is one form of nuclear reaction.
- 12. Nuclear reactions obey conservation laws. Energy stored as mass must be included in order to apply the law of conservation of energy to a nuclear reaction. Nuclear reactions must conserve electric charge. The total baryon number before and after the reaction must be the same. The total lepton number must stay the same before and after the reaction.
- 14. The nuclear reaction above is proposed for combining two atoms of silver to make an atom of gold. This reaction cannot actually happen because it breaks the rules for nuclear reactions. List two rules that are broken by the reaction.