Single Slit Diffraction - Four Wavelengths

Single Slit Diffraction - Four Wavelengths

The variation in wave intensity can be mathematically modeled. From the center of the slit, the diffracting waves propagate radially. The angle of the minimum intensity (θ_min) can be related to wavelength (λ) and the slit's width (d) such that:

dsin⁡θmin=λ.

The intensity (I) of waves at any angle can also be calculated as a relation to slit width, wavelength and intensity of the original waves before passing through the slit:

I(θ)=I0(sin⁡(πx)πx)2,

where x is equal to:

1. Elastic scattering[edit]

It is the process of changing in direction of travelling particle due to the correlation with atom. Conservation of Energy is valid and momentum is preserved.

Rutherford scattering equation

o Coulomb’s Force: electrical repulsive force is acting on α-particle and nucleus.

o Elastic collision: sum of momentum is conserved before and after.

o Rutherford scattering equation

2. Inelastic collision[edit]

Inelastic collision takes most of the part in energy loss process of charged particle inside of the matter.

Stopping power

o Atom’s ionization caused by α-particle is called inelastic collision.

o α-particle loses momentum corresponding to ionization.

o Stopping power: Energy loss due to per unit length particle in matter. It is a power that interrupts the progress of heavy particle in matter.

Range equation R = Range, E = energy of heavy particle, S = stopping power

o Linear Energy Transfer (LET): absolute value of stopping power.

o Specific Ionization: the number of ion pairs produced per unit track length.

o Bragg curve: the graph of specific energy loss along the track of a charged particle. As it loses energy, stopping power value approximately increases along the 1/E then stops. Like this, the peak before its maximum range of stopping power called Bragg peak.

o Range: distance that heavy charged particle progressed until energy is completely lost by repeating ionizing and scattering with atom. In case of the particle that has certain energy, gets certain range. Range is defined as a relation of strength of α-ray and distance.

6.2 Quantum physic

Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a fundamental branch of physics concerned with processes involving, for example, atoms and photons. Systems such as these which obey quantum mechanics can be in a quantum superposition of different states, unlike in classical physics.

Quantum mechanics gradually arose from Max Planck's solution in 1900 to the black-body radiation problem (reported 1859) and Albert Einstein's 1905 paper which offered a quantum-based theory to explain the photoelectric effect (reported 1887).Early quantum theory was profoundly reconceived in the mid-1920s.

The reconceived theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.

Important applications of quantum theory include superconducting magnets, light-emitting diodes and the laser, the transistorand semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging andelectron microscopy, and explanations for many biological and physical phenomena.

Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations.^[2] In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he later described in a paper titled On the nature of light and colours. This experiment played a major role in the general acceptance of the wave theory of light.

In 1838, Michael Faraday discovered cathode rays. These studies were followed by the 1859 statement of the black-body radiationproblem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, and the 1900 quantum hypothesis of Max Planck.^[3] Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy elements) precisely matched the observed patterns of black-body radiation.

In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation,^[4] known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it was valid only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmann's statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics.

Following Max Planck's solution in 1900 to the black-body radiation problem (reported 1859), Albert Einstein offered a quantum-based theory to explain the photoelectric effect(1905, reported 1887). Around 1900-1910, the atomic theory and the corpuscular theory of light^[5] first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation, respectively.

Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, and Pieter Zeeman, each of whom has a quantum effect named after him. Robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. At the same time, Niels Bohr developed his theory of the atomic structure, which was later confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept also introduced by Arnold Sommerfeld.^[6] This phase is known as old quantum theory.

According to Planck, each energy element (E) is proportional to its frequency (ν):

{\displaystyle E=h\nu \ }



Max Planck is considered the father of the quantum theory.

where h is Planck's constant.

Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.^[7] In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery.^[8] However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material. He won the 1921 Nobel Prize in Physics for this work.

Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle (later called the photon), with a discrete quantum of energy that was dependent on its frequency.^[9]

The 1927 Solvay Conference in Brussels.

The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein,Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Somerfield, and others. The Copenhagen interpretation of Niels Bohr became widely accepted.

In the mid-1920s, developments in quantum mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory. Out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons (1926). From Einstein's simple postulation was born a flurry of debating, theorizing, and testing. Thus, the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.^{[citation needed]}

It was found that subatomic particles and electromagnetic waves are neither simply particle nor wave but have certain properties of each. This originated the concept of wave–particle duality.^{[citation needed]}

By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann^[10] with greater emphasis on measurement, the statistical nature of our knowledge of reality, and philosophical speculation about the 'observer'. It has since permeated many disciplines including quantum chemistry, quantum electronics, quantum optics, and quantum information science. Its speculative modern developments include string theory and quantum gravity theories. It also provides a useful framework for many features of the modern periodic table of elements, and describes the behaviors of atoms during chemical bonding and the flow ofelectrons in computer semiconductors, and therefore plays a crucial role in many modern technologies.

While quantum mechanics was constructed to describe the world of the very small, it is also needed to explain some macroscopic phenomena such as superconductors, andsuperfluids.

The word quantum derives from the Latin, meaning "how great" or "how much".^[13] In quantum mechanics, it refers to a discrete unit assigned to certain physical quantities such as the energy of an atom at rest (see Figure 1). The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and subatomic systems which is today called quantum mechanics. It underlies the mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry, particle physics, nuclear chemistry, and nuclear physics. Some fundamental aspects of the theory are still actively studied.

Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller. If the physical nature of an atom were solely described byclassical mechanics, electrons would not orbit the nucleus, since orbiting electrons emit radiation (due to circular motion) and would eventually collide with the nucleus due to this loss of energy. This framework was unable to explain the stability of atoms. Instead, electrons remain in an uncertain, non-deterministic, smeared, probabilistic wave–particleorbital about the nucleus, defying the traditional assumptions of classical mechanics and electromagnetism.

Quantum mechanics was initially developed to provide a better explanation and description of the atom, especially the differences in the spectra of light emitted by differentisotopes of the same chemical element, as well as subatomic particles. In short, the quantum-mechanical atomic model has succeeded spectacularly in the realm where classical mechanics and electromagnetism falter.

6.3

The field of particle physics evolved out of nuclear physics and is typically taught in close association with nuclear physics.

The history of nuclear physics as a discipline distinct from atomic physics starts with the discovery of radioactivity by Henri Becquerel in 1896,^[1] while investigating phosphorescence in uranium salts.^[2] The discovery of the electron by J. J. Thomson^[3] a year later was an indication that the atom had internal structure. At the beginning of the 20th century the accepted model of the atom was J. J. Thomson's "plum pudding" model in which the atom was a positively charged ball with smaller negatively charged electrons embedded inside it.

In the years that followed, radioactivity was extensively investigated, notably by the husband and wife team of Pierre Curie and Marie Curie and by Ernest Rutherford and his collaborators. By the turn of the century physicists had also discovered three types of radiation emanating from atoms, which they named alpha, beta, and gamma radiation. Experiments by Otto Hahn in 1911 and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete. That is, electrons were ejected from the atom with a continuous range of energies, rather than the discrete amounts of energy that were observed in gamma and alpha decays. This was a problem for nuclear physics at the time, because it seemed to indicate that energy was not conserved in these decays.

The 1903 Nobel Prize in Physics was awarded jointly to Becquerel for his discovery and to Pierre Curie and Marie Curie for their subsequent research into radioactivity. Rutherford was awarded the Nobel Prize in Chemistry in 1908 for his "investigations into the disintegration of the elements and the chemistry of radioactive substances".

In 1905 Albert Einstein formulated the idea of mass–energy equivalence. While the work on radioactivity by Becquerel and Marie Curie predates this, an explanation of the source of the energy of radioactivity would have to wait for the discovery that the nucleus itself was composed of smaller constituents, the nucleons.

The term cosmology was first used in English in 1656 in Thomas Blount's Glossographia,^[2] and in 1731 taken up in Latin byGerman philosopher Christian Wolff, in Cosmologia Generalis.^[3]

Physical cosmology is studied by scientists, such as astronomers and physicists, as well as philosophers, such asmetaphysicians, philosophers of physics, and philosophers of space and time. Because of this shared scope with philosophy,theories in physical cosmology may include both scientific and non-scientific propositions, and may depend upon assumptions that can not be tested. Cosmology differs from astronomy in that the former is concerned with the Universe as a whole while the latter deals with individual celestial objects. Modern physical cosmology is dominated by the Big Bang theory, which attempts to bring together observational astronomy and particle physics;^[4] more specifically, a standard parameterization of the Big Bang with dark matter and dark energy, known as the Lambda-CDM model.

In Diderot's Encyclopédie, cosmology is broken down into uranology (the science of the heavens), aerology (the science of the air), geology (the science of the continents), and hydrology (the science of waters).^[7]

Metaphysical cosmology has also been described as the placing of man in the universe in relationship to all other entities. This is exemplified by Marcus Aurelius's observation that a man's place in that relationship: "He who does not know what the world is does not know where he is, and he who does not know for what purpose the world exists, does not know who he is, nor what the world is."^[8]

7.2 Astrophysics

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of theheavenly bodies, rather than their positions or motions in space."^[1][2] Among the objects studied are the Sun, other stars, galaxies,extrasolar planets, the interstellar medium and the cosmic microwave background.^[3][4] Their emissions are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, astrophysicists typically apply many disciplines of physics, including mechanics,electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.

In practice, modern astronomical research often involves a substantial amount of work in the realms of theoretical and observational physics. Some areas of study for astrophysicists include their attempts to determine: the properties of dark matter, dark energy, andblack holes; whether or not time travel is possible, wormholes can form, or the multiverse exists; and the origin and ultimate fate of the universe.^[3] Topics also studied by theoretical astrophysicists include: Solar System formation and evolution; stellar dynamics andevolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics.

Astrophysics can be studied at the bachelors, masters, and Ph.D. levels in physics or astronomy departments at many universities.

Although astronomy is as ancient as recorded history itself, it was long separated from the study of terrestrial physics. In the Aristotelianworldview, bodies in the sky appeared to be unchanging spheres whose only motion was uniform motion in a circle, while the earthly world was the realm which underwent growth and decay and in which natural motion was in a straight line and ended when the moving object reached its goal. Consequently, it was held that the celestial region was made of a fundamentally different kind of matter from that found in the terrestrial sphere; either Fire as maintained by Plato, or Aether as maintained by Aristotle.^[5][6] During the 17th century, natural philosophers such as Galileo,^[7] Descartes,^[8] and Newton^[9] began to maintain that the celestial and terrestrial regions were made of similar kinds of material and were subject to the same natural laws.^[10] Their challenge was that the tools had not yet been invented with which to prove these assertions.^[11]

For much of the nineteenth century, astronomical research was focused on the routine work of measuring the positions and computing the motions of astronomical objects.^[12][13] A new astronomy, soon to be called astrophysics, began to emerge when William Hyde Wollaston andJoseph von Fraunhofer independently discovered that, when decomposing the light from the Sun, a multitude of dark lines (regions where there was less or no light) were observed in the spectrum.^[14] By 1860 the physicist, Gustav Kirchhoff, and the chemist, Robert Bunsen, had demonstrated that the dark lines in the solar spectrum corresponded to bright lines in the spectra of known gases, specific lines corresponding to unique chemical elements.^[15] Kirchhoff deduced that the dark lines in the solar spectrum are caused by absorption bychemical elements in the Solar atmosphere.^[16] In this way it was proved that the chemical elements found in the Sun and stars were also found on Earth.

Among those who extended the study of solar and stellar spectra was Norman Lockyer, who in 1868 detected bright, as well as dark, lines in solar spectra. Working with the chemist, Edward Frankland, to investigate the spectra of elements at various temperatures and pressures, he could not associate a yellow line in the solar spectrum with any known elements. He thus claimed the line represented a new element, which was called helium, after the GreekHelios, the Sun personified.^[17][18]

In 1885, Edward C. Pickering undertook an ambitious program of stellar spectral classification at Harvard College Observatory, in which a team of woman computers, notablyWilliamina Fleming, Antonia Maury, and Annie Jump Cannon, classified the spectra recorded on photographic plates. By 1890, a catalog of over 10,000 stars had been prepared that grouped them into thirteen spectral types. Following Pickering's vision, by 1924 Cannon expanded the catalog to nine volumes and over a quarter of a million stars, developing the Harvard Classification Scheme which was accepted for world-wide use in 1922.^[19]

In 1895, George Ellery Hale and James E. Keeler, along with a group of ten associate editors from Europe and the United States,^[20] established The Astrophysical Journal: An International Review of Spectroscopy and Astronomical Physics.^[21] It was intended that the journal would fill the gap between journals in astronomy and physics, providing a venue for publication of articles on astronomical applications of the spectroscope; on laboratory research closely allied to astronomical physics, including wavelength determinations of metallic and gaseous spectra and experiments on radiation and absorption; on theories of the Sun, Moon, planets, comets, meteors, and nebulae; and on instrumentation for telescopes and laboratories.^[20]

In 1925 Cecilia Helena Payne (later Cecilia Payne-Gaposchkin) wrote an influential doctoral dissertation at Radcliffe College, in which she applied ionization theory to stellar atmospheres to relate the spectral classes to the temperature of stars.^[22] Most significantly, she discovered that hydrogen and helium were the principal components of stars. This discovery was so unexpected that her dissertation readers convinced her to modify the conclusion before publication. However, later research confirmed her discovery.^[23]

By the end of the 20th century, further study of stellar and experimental spectra advanced, particularly as a result of the advent of quantum physics.^[24]

• Protons: A proton is a positively charged particle in an atom’s nucleus. The nucleus is the dense center of an atom

. • Neutrons: A neutron has no electrical charge, has about the same mass as a proton, and is also found in an atom’s nucleus.

• Electrons: An electron is a negatively charged particle found outside the nucleus. Electrons are much smaller than either protons or neutrons. Different types of atoms are called elements, which cannot be broken down by ordinary chemical means. Which element an atom is depends on the number of protons in the atom’s nucleus. For example, all hydrogen atoms have one proton, and all oxygen atoms have 16 protons. Only about 25 different elements are found in organisms. Atoms of different elements can link, or bond, together to form compounds. Atoms form bonds in two ways.

• Ionic bonds: An ion is an atom that has gained or lost one or more electrons. Some atoms form positive ions, which happens when an atom loses electrons. Other atoms form negative ions, which happens when an atom gains electrons. An ionic bond forms through the electrical force between oppositely charged ions. [1]

• Covalent bonds: A covalent bond forms when atoms share one or more pairs of electrons. A molecule is two or more atoms that are held together by covalent bonds.

2.1 Laws of Chemical Combination—The basic laws of chemical combination are the law of conservation of mass, the law of constant composition, and the law of multiple proportions. Each played an important role in Dalton’s development of the atomic theory.

2.2 John Dalton and the Atomic Theory of Matter—Dalton developed his atomic theory to account for the basic laws of chemical combination. The theory centered around the existence of indivisible small particles of matter called atoms and addressed the unique nature of chemical elements, the formation of chemical compounds from atoms of different elements, and the atomic nature of chemical reactions.

2.3 The Divisible Atom—Of the fundamental particles found in atoms, the three of most concern to chemists are protons, neutrons, and electrons. Protons and neutrons make up the nucleus, and their combined number is the mass number, A, of the atom. The number of protons is the atomic number, Z. Electrons are found outside the nucleus, and their number is also equal to the atomic number. The negative charge on an electron is equal in magnitude to the positive charge on a proton. All atoms of an element have the same atomic number, but they may have different numbers of neutrons and hence different mass numbers. Atoms containing the same number of protons (atomic number) but different numbers of neutrons (mass number) are isotopes of an element. Chemical symbols for isotopes are commonly written in the form  with Abeing the mass number and Z the atomic number of the element E.

2.4 Atomic Masses—The atomic mass of an element is a weighted average value calculated from the masses and relative abundances of its naturally occurring isotopes. Theatomic mass unit represents the standard unit of measure of atomic masses; it is exactly  of the mass of a carbon-12 atom.

2.5 The Periodic Table: Elements Organized—The periodic table is an arrangement of the elements by atomic number into rows and columns. This arrangement places elements having similar properties in the same vertical groups (families). This arrangement also allows for the classification of elements as metal, nonmetal, or metalloid.

2.6 Molecules and Molecular Compounds—A chemical formula, the generic term for the various notations used to represent compounds, indicates the relative numbers of atoms of each type in a compound. An empirical formula expresses the simplest atom ratio, and a molecular formula reflects the actual composition of a molecule.Structural formulas describe the arrangement of atoms within molecules. Molecular models are also used to represent the structure and shape of molecules. For example, for acetic acid:

A molecular compound consists of molecules. In a binary molecular compound, the molecules are made up of atoms of two elements. In naming these compounds, the numbers of atoms in the molecules are denoted by prefixes; the names also feature -ide endings.

2.7 Ions and Ionic Compounds—Ions are formed by the loss or gain of electrons by single atoms or groups of atoms. Positive ions are cations, and negative ions areanions. An ionic compound is made up of cations and anions held together by electrostatic attractions. Chemical formulas of ionic compounds are based on an electrically neutral combination of cations and anions called a formula unit, such as NaCl.

2.9 Organic Compounds—Organic compounds are based on the element carbon. Hydrocarbons contain only hydrogen and carbon. Alkanes have carbon atoms joined together by single bonds into chains or rings, with hydrogen atoms attached to the carbon atoms. Alkanes with four or more carbon atoms can exist as isomers, which are molecules that have the same molecular formula but different structures and properties.