Download NUCLEAR PHYSICS

NUCLEAR PHYSICS
1.
State and explain Pauli's exclusion principle.
The three types of particles from which the ordinary atom is made—protons, electrons,
and neutrons—are all subject to it, and the structure and chemical behavior of atoms is due to it.
It causes atoms to take up the space they do, since electrons cannot all congregate in the lowestenergy state but must occupy higher energy states at a distance from lower-energy electrons,
therefore matter made of atoms occupies space rather than being condensed. As such, the Pauli
exclusion principle underpins many properties of everyday matter, from its large-scale stability to
the periodic table of the elements.
Fermions, particles with antisymmetric wave functions, obey the Pauli exclusion principle. In
addition to the electron, proton and neutron, these include neutrinos and quarks (the constituent
particles of protons and neutrons), and some atoms such as helium-3. All fermions have "halfinteger spin", i.e. their intrinsic angular momentum value is
(reduced Planck's
constant) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics fermions
are described by antisymmetric states. Particles with integer spin (called bosons) have symmetric
wave functions; unlike fermions they may share the same quantum states. Bosons include
the photon, the Cooper pairs which are responsible for superconductivity, and the W and Z
bosons. (Fermions take their name from the Fermi–Dirac statistical distribution that they obey,
and bosons from their Bose–Einstein distribution).
[edit]History
In the early 20th century it became evident that atoms and molecules with even numbers of
electrons are more chemically stable than those with odd numbers of electrons. In the famous
1916 articleThe Atom and the Molecule by Gilbert N. Lewis, for example, the third of his six
postulates of chemical behavior states that the atom tends to hold an even number of electrons in
the shell and especially to hold eight electrons which are normally arranged symmetrically at the
eight corners of a cube (see: cubical atom). In 1919 chemist Irving Langmuir suggested that
the periodic table could be explained if the electrons in an atom were connected or clustered in
some manner. Groups of electrons were thought to occupy a set of electron shells about the
nucleus.[1] In 1922, Niels Bohrupdated his model of the atom by assuming that certain numbers of
electrons (for example 2, 8 and 18) corresponded to stable "closed shells".
Pauli looked for an explanation for these numbers, which were at first only empirical. At the same
time he was trying to explain experimental results in the Zeeman effect in atomic
spectroscopy and inferromagnetism. He found an essential clue in a 1924 paper by Edmund C.
Stoner which pointed out that for a given value of the principal quantum number (n), the number
of energy levels of a single electron in the alkali metal spectra in an external magnetic field,
where all degenerate energy levels are separated, is equal to the number of electrons in the
closed shell of the rare gases for the same value of n. This led Pauli to realize that the
complicated numbers of electrons in closed shells can be reduced to the simple rule of one per
state, if the electron states are defined using four quantum numbers. For this purpose he
introduced a new two-valued quantum number, identified by Samuel Goudsmit and George
Uhlenbeck as electron spin.
2. Explain how this principle is used to determine the electronic configuration of
atoms.
In atomic physics and quantum chemistry, electron configuration is the arrangement
of electrons of an atom, a molecule, or other physical structure.[1] It concerns the way electrons
can be distributed in the orbitals of the given system (atomic or molecular for instance).
Like the other elementary particles, the electron is subject to the laws of quantum mechanics, and
exhibits both particle-like and wave-like nature. Formally, the quantum state of a particular
electron is defined by its wave function, a complex-valued function of space and time. According
to the Copenhagen interpretation of quantum mechanics, the position of a particular electron is
not well defined until an act of measurement causes it to be detected. The probability that the act
of measurement will detect the electron at a particular point in space is proportional to the square
of the absolute value of the wavefunction at that point.
An energy is associated with each electron configuration and, upon certain conditions, electrons
are able to move from one orbital to another by emission or absorption of a quantum of energy, in
the form of a photon.
Knowledge of the electron configuration of different atoms is useful in understanding the structure
of the periodic table of elements. The concept is also useful for describing the chemical bonds
that hold atoms together. In bulk materials this same idea helps explain the peculiar properties
of lasers and semiconductors.
Physicists and chemists use a standard notation to indicate the electron configurations of atoms
and molecules. For atoms, the notation consists of a sequence of atomic orbital labels (e.g.
forphosphorus the sequence 1s, 2s, 2p, 3s, 3p) with the number of electrons assigned to each
orbital (or set of orbitals sharing the same label) placed as a superscript. For
example, hydrogen has one electron in the s-orbital of the first shell, so its configuration is written
1s1. Lithium has two electrons in the 1s-subshell and one in the (higher-energy) 2s-subshell, so
its configuration is written 1s2 2s1(pronounced "one-s-two, two-s-one"). Phosphorus (atomic
number 15), is as follows: 1s2 2s2 2p6 3s2 3p3.
For atoms with many electrons, this notation can become lengthy and so an abbreviated notation
is used, since all but the last few subshells are identical to those of one or another of the noble
gases. Phosphorus, for instance, differs from neon (1s2 2s2 2p6) only by the presence of a third
shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows:
[Ne] 3s2 3p3. This convention is useful as it is the electrons in the outermost shell which most
determine the chemistry of the element.
The order of writing the orbitals is not completely fixed: some sources group all orbitals with the
same value of n together, while other sources (as here) follow the order given by Madelung's rule.
Hence the electron configuration of iron can be written as [Ar] 3d6 4s2 (keeping the 3d-electrons
with the 3s- and 3p-electrons which are implied by the configuration of argon) or as
[Ar] 4s2 3d6 (following the Aufbau principle, see below).
3.
Write an account on LS coupling.
In quantum mechanics, the procedure of constructing eigenstates of total angular momentum
out of eigenstates of separate angular momenta is called angular momentum coupling. For
instance, the orbit and spin of a single particle can interact through spin-orbit interaction, in which
case the complete physical picture must include spin-orbit coupling. Or two charged particles,
each with a well-defined angular momentum, may interact by Coulomb forces, in which case
coupling of the two one-particle angular momenta to a total angular momentum is a useful step in
the solution of the two-particle Schrödinger equation. In both cases the separate angular
momenta are no longer constants of motion, but the sum of the two angular momenta usually still
is. Angular momentum coupling in atoms is of importance in atomic spectroscopy. Angular
momentum coupling of electron spins is of importance in quantum chemistry. Also in the nuclear
shell model angular momentum coupling is ubiquitous.
In astronomy, spin-orbit coupling reflects the general law of conservation of angular
momentum, which holds for celestial systems as well. In simple cases, the direction of
the angular momentum vector is neglected, and the spin-orbit coupling is the ratio between the
frequency with which a planet or other celestial bodyspins about its own axis to that with which it
orbits another body. This is more commonly known as orbital resonance. Often, the underlying
physical effects are tidal forces.
Conservation of angular momentum is the principle that the total angular momentum of a system
has a constant magnitude and direction if the system is subjected to no external force. Angular
momentum is a property of a physical system that is a constant of motion[1] (is time-independent
and well-defined) in two situations: (i) The system experiences a spherically symmetric potential
field. (ii) The system moves (in quantum mechanical sense) in isotropic space. In both cases the
angular momentum operator commutes with the Hamiltonian of the system. By
Heisenberg's uncertainty relation this means that the angular momentum can assume a sharp
value simultaneously with the energy (eigenvalue of the Hamiltonian).
An example of the first situation is an atom whose electrons only feel the Coulomb field of its
nucleus. If we ignore the electron-electron interaction (and other small interactions such as spinorbit coupling), the orbital angular momentum l of each electron commutes with the total
Hamiltonian. In this model the atomic Hamiltonian is a sum of kinetic energies of the electrons
and the spherically symmetric electron-nucleus interactions. The individual electron angular
momenta l(i) commute with this Hamiltonian. That is, they are conserved properties of this
approximate model of the atom.
An example of the second situation is a rigid rotor moving in field-free space. A rigid rotor has a
well-defined, time-independent, angular momentum.
These two situations originate in classical mechanics. The third kind of conserved angular
momentum, associated with spin, does not have a classical counterpart. However, all rules of
angular momentum coupling apply to spin as well.
4. Explain the various methods of detecting neurons.
Functional magnetic resonance imaging (fMRI) is one of the most widely
used methods to study neuronal activity in human brain in vivo. A datadriven method is proposed to detect both the temporal and spatial
information in fMRI data acquired during the representation of stimuli,
which may also be applied when the expected response cannot be
estimated a priori. The method is built on the existing temporal clustering
analysis technique with additional features of searching for the connected
components in the temporal and spatial domains in the whole brain.
Moreover, no pre-defined assumptions about the stimuli are required in
comparison to the previous methods. The output contains the information
on how long the activation sustains and where the corresponding voxels
are. For validation, the method has been applied to four sets of data from
an experiment involving visual stimuli. Our method is able to detect the
response to the stimuli.
First-order motion perception
refers to the perception of the motion of an object that differs in luminance from its background,
such as a black bug crawling across a white page. This sort of motion can be detected by a
relatively simple motion sensor designed to detect a change in luminance at one point on the
retina and correlate it with a change in luminance at a neighbouring point on the retina after a
delay. Sensors that work this way have been referred to asHassenstein-Reichardt detectors after
the scientists Bernhard Hassenstein, behaviour analyses and Werner Reichardt, who first
modelled them.[4] motion-energy sensors,[5] or Elaborated Reichardt Detectors.[6] These sensors
detect motion by spatio-temporal correlation and are plausible models for how the visual system
may detect motion. There is still considerable debate regarding the exact nature of this process.
First-order motion sensors suffer from theaperture problem, which means that they can detect
motion only perpendicular to the orientation of the contour that is moving. Further processing is
required to disambiguate true global motion direction.[7]
5. Explain the plasma confinement phenomenon.
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of
the particles are ionized. Heating a gas mayionize its molecules or atoms (reduce or increase the
number of electrons in them), thus turning it into a plasma, which contains chargedparticles:
positive ions and negative electrons or ions.[1] Ionization can be induced by other means, such as
strong electromagnetic field applied with a laser or microwave generator, and is accompanied by
the dissociation of molecular bonds, if present.[2]
The presence of a non-negligible number of charge carriers makes the plasma electrically
conductive so that it responds strongly toelectromagnetic fields. Plasma, therefore, has properties
quite unlike those of solids, liquids, or gases and is considered a distinct state of matter. Like gas,
plasma does not have a definite shape or a definite volume unless enclosed in a container; unlike
gas, under the influence of a magnetic field, it may form structures such as filaments, beams
and double layer. Some common plasmas are stars and neon signs. In theuniverse, plasma is the
most common state of matter for ordinary matter, most of which is in the rarefied intergalactic
plasma (particularlyintracluster medium) and in stars.
Definition of a plasma
Plasma is loosely described as an electrically neutral medium of positive and negative particles
(i.e. the overall charge of a plasma is roughly zero). It is important to note that although they are
unbound, these particles are not ‘free’. When the charges move they generate electrical currents
with magnetic fields, and as a result, they are affected by each other’s fields. This governs their
collective behavior with many degrees of freedom.[2][6] A definition can have three criteria:[7][8]
1. The plasma approximation: Charged particles must be close enough together that each
particle influences many nearby charged particles, rather than just interacting with the
closest particle (these collective effects are a distinguishing feature of a plasma). The
plasma approximation is valid when the number of charge carriers within the sphere of
influence (called the Debye sphere whose radius is the Debye screening length) of a
particular particle is higher than unity to provide collective behavior of the charged
particles. The average number of particles in the Debye sphere is given by the plasma
parameter, "Λ" (the Greek letter Lambda).
2. Bulk interactions: The Debye screening length (defined above) is short compared to the
physical size of the plasma. This criterion means that interactions in the bulk of the
plasma are more important than those at its edges, where boundary effects may take
place. When this criterion is satisfied, the plasma is quasineutral.
3. Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the
electrons) is large compared to the electron-neutral collision frequency (measuring
frequency of collisions between electrons and neutral particles). When this condition is
valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.
6. Discuss the various conservation laws associated with fundamental particles.
7. State and explain CPT theorem.
Efforts during the late 1950s revealed the violation of P-symmetry by phenomena that involve
the weak force, and there were well-known violations of C-symmetry as well. For a short time,
the CP-symmetry was believed to be preserved by all physical phenomena, but that was later
found to be false too, which implied, by CPT invariance, violations of T-symmetry as well.
The CPT theoremrequires the preservation of CPT symmetry by all physical phenomena. It
assumes the correctness of quantum laws and Lorentz invariance. Specifically, the CPT theorem
states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must
have CPT symmetry.
The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to
prove the connection between spin and statistics. In 1954, Gerhart Lüders and Wolfgang
Pauli derived more explicit proofs, so this theorem is sometimes known as the Lüders-Pauli
theorem. At about the same time, and independently, this theorem was also proved by John
Stewart Bell. These proofs are based on the validity of Lorentz invariance and the Principle of
locality in the interaction of quantum fields. Subsequently Res Jost gave a more general proof in
the framework of axiomatic quantum field theory.
[edit]Derivation
Consider a Lorentz boost in a fixed direction z. This can be interpreted as a rotation of the time
axis into the z axis, with an imaginary rotation parameter. If this rotation parameter were real, it
would be possible for a 180° rotation to reverse the direction of time and of z. Reversing the
direction of one axis is a reflection of space in any number of dimensions. If space has 3
dimensions, it is equivalent to reflecting all the coordinates, because an additional rotation of 180°
in the x-y plane could be included.
This defines a CPT transformation if we adopt the Feynman-Stueckelberg interpretation of
antiparticles as the corresponding particles traveling backwards in time. This interpretation
requires a slightanalytic continuation, which is well-defined only under the following assumptions:
1. The theory is Lorentz invariant;
2. The vacuum is Lorentz invariant;
3. The energy is bounded below.
When the above hold, quantum theory can be extended to a Euclidean theory, defined by
translating all the operators to imaginary time using the Hamiltonian. The commutation
relations of the Hamiltonian, and the Lorentz generators, guarantee that Lorentz
invariance implies rotational invariance, so that any state can be rotated by 180 degrees.
Since a sequence of two CPT reflections is equivalent to a 360-degree rotation, fermions change
by a sign under two CPT re
8.
Define atomic scattering factor. Obtain an expression for it.