Atomic structure and energy levels in applied physics pdf
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- Hydrogen atom
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A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. In everyday life on Earth, isolated hydrogen atoms called "atomic hydrogen" are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary diatomic hydrogen gas, H 2.
For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen which would refer to isolated hydrogen atoms. Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen or any atom can exist, contrary to the predictions of classical physics.
Attempts to develop a theoretical understanding of the states of the hydrogen atom have been important to the history of quantum mechanics , since all other atoms can be roughly understood by knowing in detail about this simplest atomic structure.
The most abundant isotope , hydrogen-1 , protium , or light hydrogen , contains no neutrons and is simply a proton and an electron. Protium is stable and makes up Deuterium contains one neutron and one proton in its nucleus. Deuterium is stable and makes up 0. Tritium contains two neutrons and one proton in its nucleus and is not stable, decaying with a half-life of Because of its short half-life, tritium does not exist in nature except in trace amounts.
They are unbound resonances located beyond the neutron drip line ; this results in prompt emission of a neutron. The formulas below are valid for all three isotopes of hydrogen, but slightly different values of the Rydberg constant correction formula given below must be used for each hydrogen isotope.
Lone neutral hydrogen atoms are rare under normal conditions. However, neutral hydrogen is common when it is covalently bound to another atom, and hydrogen atoms can also exist in cationic and anionic forms.
If a neutral hydrogen atom loses its electron, it becomes a cation. Free protons are common in the interstellar medium , and solar wind. If instead a hydrogen atom gains a second electron, it becomes an anion. The hydrogen anion is written as "H — " and called hydride.
The hydrogen atom has special significance in quantum mechanics and quantum field theory as a simple two-body problem physical system which has yielded many simple analytical solutions in closed-form.
Experiments by Ernest Rutherford in showed the structure of the atom to be a dense, positive nucleus with a tenuous negative charge cloud around it. This immediately raised questions about how such a system could be stable. Classical electromagnetism had shown that any accelerating charge radiates energy, as shown by the Larmor formula.
If the electron is assumed to orbit in a perfect circle and radiates energy continuously, the electron would rapidly spiral into the nucleus with a fall time of: .
If this were true, all atoms would instantly collapse, however atoms seem to be stable. Furthermore, the spiral inward would release a smear of electromagnetic frequencies as the orbit got smaller. Instead, atoms were observed to only emit discrete frequencies of radiation. The resolution would lie in the development of quantum mechanics.
In , Niels Bohr obtained the energy levels and spectral frequencies of the hydrogen atom after making a number of simple assumptions in order to correct the failed classical model. The assumptions included:. He also supposed that the centripetal force which keeps the electron in its orbit is provided by the Coulomb force , and that energy is conserved. Bohr derived the energy of each orbit of the hydrogen atom to be: .
Bohr's predictions matched experiments measuring the hydrogen spectral series to the first order, giving more confidence to a theory that used quantized values. The exact value of the Rydberg constant assumes that the nucleus is infinitely massive with respect to the electron.
For hydrogen-1, hydrogen-2 deuterium , and hydrogen-3 tritium which have finite mass, the constant must be slightly modified to use the reduced mass of the system, rather than simply the mass of the electron. This includes the kinetic energy of the nucleus in the problem, because the total electron plus nuclear kinetic energy is equivalent to the kinetic energy of the reduced mass moving with a velocity equal to the electron velocity relative to the nucleus.
However, since the nucleus is much heavier than the electron, the electron mass and reduced mass are nearly the same. The Rydberg constant R M for a hydrogen atom one electron , R is given by. These figures, when added to 1 in the denominator, represent very small corrections in the value of R , and thus only small corrections to all energy levels in corresponding hydrogen isotopes.
Most of these shortcomings were resolved by Arnold Sommerfeld's modification of the Bohr model. Sommerfeld introduced two additional degrees of freedom, allowing an electron to move on an elliptical orbit characterized by its eccentricity and declination with respect to a chosen axis. This introduced two additional quantum numbers, which correspond to the orbital angular momentum and its projection on the chosen axis.
Thus the correct multiplicity of states except for the factor 2 accounting for the yet unknown electron spin was found. Further, by applying special relativity to the elliptic orbits, Sommerfeld succeeded in deriving the correct expression for the fine structure of hydrogen spectra which happens to be exactly the same as in the most elaborate Dirac theory.
However, some observed phenomena, such as the anomalous Zeeman effect , remained unexplained. These issues were resolved with the full development of quantum mechanics and the Dirac equation.
This is not the case, as most of the results of both approaches coincide or are very close a remarkable exception is the problem of hydrogen atom in crossed electric and magnetic fields, which cannot be self-consistently solved in the framework of the Bohr—Sommerfeld theory , and in both theories the main shortcomings result from the absence of the electron spin. It was the complete failure of the Bohr—Sommerfeld theory to explain many-electron systems such as helium atom or hydrogen molecule which demonstrated its inadequacy in describing quantum phenomena.
Exact analytical answers are available for the nonrelativistic hydrogen atom. Before we go to present a formal account, here we give an elementary overview. The lowest energy equilibrium state of the hydrogen atom is known as the ground state. It is written as:. Then we say that the wavefunction is properly normalized. The Hamiltonian of the hydrogen atom is the radial kinetic energy operator and Coulomb attraction force between the positive proton and negative electron.
Expanding the Laplacian in spherical coordinates:. This is a separable , partial differential equation which can be solved in terms of special functions. The normalized position wavefunctions , given in spherical coordinates are:. Additionally, these wavefunctions are normalized i. The wavefunctions in momentum space are related to the wavefunctions in position space through a Fourier transform.
It also yields two other quantum numbers and the shape of the electron's wave function "orbital" for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds.
When there is more than one electron or nucleus the solution is not analytical and either computer calculations are necessary or simplifying assumptions must be made. The Dirac equation of relativistic quantum theory improves these solutions see below. Although the resulting energy eigenfunctions the orbitals are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian that is, the energy eigenstates can be chosen as simultaneous eigenstates of the angular momentum operator.
This corresponds to the fact that angular momentum is conserved in the orbital motion of the electron around the nucleus. In addition to mathematical expressions for total angular momentum and angular momentum projection of wavefunctions, an expression for the radial dependence of the wave functions must be found. The principal quantum number in hydrogen is related to the atom's total energy. Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.
According to the usual rules of quantum mechanics, the actual state of the electron may be any superposition of these states. In , Paul Dirac found an equation that was fully compatible with special relativity , and as a consequence made the wave function a 4-component " Dirac spinor " including "up" and "down" spin components, with both positive and "negative" energy or matter and antimatter.
The energy levels of hydrogen, including fine structure excluding Lamb shift and hyperfine structure , are given by the Sommerfeld fine structure expression: . It is worth noting that this expression was first obtained by A.
Sommerfeld in based on the relativistic version of the old Bohr theory. Sommerfeld has however used different notation for the quantum numbers. The coherent states have been proposed as . The image to the right shows the first few hydrogen atom orbitals energy eigenfunctions.
These are cross-sections of the probability density that are color-coded black represents zero density and white represents the highest density.
For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz -plane z is the vertical axis. The probability density in three-dimensional space is obtained by rotating the one shown here around the z -axis. The " ground state ", i.
Black lines occur in each but the first orbital: these are the nodes of the wavefunction, i. The quantum numbers determine the layout of these nodes. Both of these features and more are incorporated in the relativistic Dirac equation , with predictions that come still closer to experiment. Again the Dirac equation may be solved analytically in the special case of a two-body system, such as the hydrogen atom.
The resulting solution quantum states now must be classified by the total angular momentum number j arising through the coupling between electron spin and orbital angular momentum.
States of the same j and the same n are still degenerate. For these developments, it was essential that the solution of the Dirac equation for the hydrogen atom could be worked out exactly, such that any experimentally observed deviation had to be taken seriously as a signal of failure of the theory.
In the language of Heisenberg's matrix mechanics , the hydrogen atom was first solved by Wolfgang Pauli  using a rotational symmetry in four dimensions [O 4 -symmetry] generated by the angular momentum and the Laplace—Runge—Lenz vector. By extending the symmetry group O 4 to the dynamical group O 4,2 , the entire spectrum and all transitions were embedded in a single irreducible group representation. In the non-relativistic hydrogen atom was solved for the first time within Feynman's path integral formulation of quantum mechanics by Duru and Kleinert.
From Wikipedia, the free encyclopedia. Atom of the element hydrogen. This article is about the physics of the hydrogen atom. For a chemical description, see hydrogen. Main article: Isotopes of hydrogen. Main articles: hydrogen cation and hydrogen anion. Main article: Bohr model. Main article: Hydrogen-like atom.
[PDF] Applied Physics Study Material
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. In everyday life on Earth, isolated hydrogen atoms called "atomic hydrogen" are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary diatomic hydrogen gas, H 2. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen which would refer to isolated hydrogen atoms. Atomic spectroscopy shows that there is a discrete infinite set of states in which a hydrogen or any atom can exist, contrary to the predictions of classical physics. Attempts to develop a theoretical understanding of the states of the hydrogen atom have been important to the history of quantum mechanics , since all other atoms can be roughly understood by knowing in detail about this simplest atomic structure.
Atomic Physics Ppt. Atomic Physics, P. We usually admit about 50 students from over applicants from all over the world each year. These atoms can join together to form molecules. If it is an atom, remember to subtract the mass of electrons. Atomic Structure Powerpoint. Departmental Colloquia are usually on Tuesdays or Thursdays at hrs.
Along with this, I will also try to provide download links of some of the top physics textbooks in pdf format. The most commonly used semiconductor element is A. Commonly Questions asked in Physics with answers. The basic computer knowledge practice problem section will get you the required practice and experience. This subject is common for all branches for the first year engineering students. Copper is a A.
Atomic Physics Ppt
In this chapter, we use quantum mechanics to study the structure and properties of atoms. This study introduces ideas and concepts that are necessary to understand more complex systems, such as molecules, crystals, and metals. Ultraviolet light from hot stars ionizes the hydrogen atoms in the nebula. As protons and electrons recombine, radiation of different frequencies is emitted. The details of this process can be correctly predicted by quantum mechanics and are examined in this chapter.
Thompson PPT. Physics is a natural science that involves the study of matter and its motion through space-time, along with related concepts such as energy and force. Because atoms are far too small to see, their structure has always been something of a mystery.
An isolated atom possesses discrete energies of different electrons. Suppose two isolated atoms are brought to very close proximity, then the electrons in the orbits of two atoms interact with each other. So, that in the combined system, the energies of electrons will not be in the same level but changes and the energies will be slightly lower and larger than the original value. So, at the place of each energy level, a closely spaced two energy levels exists.
Atomic Structure And Energy Levels In Applied Physics Pdf
Atomic periodic structure. The Harmonic Oscillator Potential. Identical particles. Bosons, fermions. Schrodinger equation are now only a discrete set of possible values a discrete set os energy levels.
Figure 1. In , after returning to Copenhagen, he began publishing his theory of the simplest atom, hydrogen, based on the planetary model of the atom. For decades, many questions had been asked about atomic characteristics. From their sizes to their spectra, much was known about atoms, but little had been explained in terms of the laws of physics.
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