LIST OF QUESTIONS FOR ENDTERM 1.Thermal radiation, model of absolute blackbody.

thermal radiation, process by which energy, in the form of electromagnetic radiation, is emitted by a heated surface in all directions and travels directly to its point of absorption at the speed of light; thermal radiation does not require an intervening medium to carry it.

Thermal radiation ranges in wavelength from the longest infrared rays through the visible-light spectrum to the shortest ultraviolet rays. The intensity and distribution of radiant energy within this range is governed by the temperature of the emitting surface. The total radiant heat energy emitted by a surface is proportional to the fourth power of its absolute temperature (the Stefan–Boltzmann law).

The rate at which a body radiates (or absorbs) thermal radiation depends upon the nature of the surface as well. Objects that are good emitters are also good absorbers (Kirchhoff’s radiation law). A blackened surface is an excellent emitter as well as an excellent absorber. If the same surface is silvered, it becomes a poor emitter and a poor absorber. A blackbody is one that absorbs all the radiant energy that falls on it. Such a perfect absorber would also be a perfect emitter.

The heating of the Earth by the Sun is an example of transfer of energy by radiation. The heating of a room by an open-hearth fireplace is another example. The flames, coals, and hot bricks radiate heat directly to the objects in the room with little of this heat being absorbed by the intervening air. Most of the air that is drawn from the room and heated in the fireplace does not reenter the room in a current of convection but is carried up the chimney together with the products of combustion.

A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black.

In practice no material has been found to absorb all incoming radiation, but carbon in its graphite form absorbs all but about 3%. It is also a perfect emitter of radiation. At a particular temperature the black body would emit the maximum amount of energy possible for that temperature. This value is known as the black body radiation. It would emit at every wavelength of light as it must be able to absorb every wavelength to be sure of absorbing all incoming radiation. The maximum wavelength emitted by a black body radiator is infinite. It also emits a definite amount of energy at each wavelength for a particular temperature, so standard black body radiation curves can be drawn for each temperature, showing the energy radiated at each wavelength. All objects emit radiation above absolute zero.2.Stefan-Boltzmann law.

In quantum physics, the Stefan-Boltzmann law (sometimes called Stefan's Law) states that the energy radiated by a blackbody is directly proportional to the temperature of the object raised to the fourth power. The equation for this law is:

R=σT4

where σ is the Stefan-Boltzmann constant, which is equal to 5.670 373(21) x 10-8 W m-2 K-4, and where R is the energy radiated per unit surface area and per unit time. T is temperature, which is measured in Kelvin scale. Although this law is accurate and helpful, it is only usable for the energy radiated by blackbodies.

3.Wien’s deviation law, Rayleigh-Jeans law, Ultraviolet catastrophe, Plank’s hypothesis.

Wien's displacement law states that the wavelength distribution of thermal radiation from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced on the graph. Apart from an overall T4 multiplicative factor, the average thermal energy in each mode with frequency ν only depends on the ratio ν/T. Restated in terms of the wavelength λ = c/ν, the distributions at corresponding wavelengths are related, where corresponding wavelengths are at locations proportional to 1/T. Blackbody radiation approximates to Wien's law at high frequency.

From this general law, it follows that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength, and this less powerful consequence is often also called Wien's displacement law in many textbooks.

\lambda_\text{max} T = b,where λmax is the peak wavelength, T is the absolute temperature of the black body, and b is a constant of proportionality called Wien's displacement constant, equal to 2.8977721(26)×10−3 m K.

4.The Photoelectric Effect: Experiment, Cut-off Frequency, Einstein’s formula, application of this effect.

5.Compton Scattering.

Compton scattering, or the Compton effect, is the name used for what happens to the energy (or frequency or wavelength) of an X-ray or gamma ray photon when it interacts with matter; the wavelength increases (or energy/frequency decreases) as it scatters off electrons. This scattering is one of the main things that happen when gamma rays meet matter.

6.De Broglie’s Hypothesis .   Interference Pattern of Electrons.   Длина волны квантовой частицы обратно пропорциональна ее импульсу.

In his 1923 (or 1924, depending on the source) doctoral dissertation, the French physicist Louis de Broglie made a bold assertion. Considering Einstein's relationship of wavelength lambda to momentum p, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:lambda = h / p

This wavelength is called the de Broglie wavelength. The reason he chose the momentum equation over the energy equation is that it was unclear, with matter, whether E should be total energy, kinetic energy, or total relativistic energy. For photons they are all the same, but not so for matter.The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons.

Physicists who studied light in the 1700s and 1800s were having a big argument about whether light was made of particles shooting around like tiny bullets, or waves washing around like water waves. At times, light seems to do both. At times, light seems to go only in a straight line, as if it were made of particles. But other experiments show that light has a frequency and wavelength, just like a sound wave or water wave. Until the 20th century, most physicists thought that light was either one or the other, and that the scientists on the other side of the argument were simply wrong.

To make matters even more confusing, Louis de Broglie suggested that matter might act the same way. Scientists then performed these same experiments with electrons, and found that electrons too are somehow both particles and waves. Electrons can be used to do Young's double-slit experiment.

Today, these experiments have been done in so many different ways by so many different people that scientists simply accept that both matter and light are somehow both waves and particles. This seeming impossibility is referred to as the wave-particle duality.7.Electron microscope.

An electron microscope is a scientific instrument which uses a beam of electrons to examine objects on a very fine scale. In an optical microscope, the wavelength of light limits the maximum magnification that is possible. As electrons have a smaller wavelength, they can

achieve a higher magnification, and can see very small objects - typically around 1,000 times smaller than those seen in an optical microscope. The outline of objects, as revealed by the flow of electrons, is changed into a picture using visible light for people to see.

8.Uncertainty Principle. The wave Particle Duality and Complementarities. Plank’s constant.

No thing has a definite position, a definite trajectory, or a definite momentum. Trying to pin a thing down to one definite position will make its momentum less well pinned down, and vice-versa. In everyday life we can successfully measure the position of an automobile at a definite time and then measure its direction and speed (assuming it is coasting along at a steady rate) in the next few moments. That is because the uncertainties in position and velocity are so small that we could not detect them. 

We may bring that experience to the world of atomic-sized phenomena and incorrectly assume that if we measure the position of something like an electron as it moves along its trajectory it will continue to move along that same trajectory, which we imagine we can then accurately detect in the next few moments. We need to learn that the electron did not have a definite position before we located it, and that it also did not have a definite momentum before we measured the trajectory. Moreover, we may justifiably assume that a photon produced by a laser aimed at a detection screen will hit very near to its target on that screen, and confirm this prediction by any number of experiments. Next we will discover that the more closely we try to pin down some location for the electron on its way toward the detection screen, the more it and all others like it will be likely to miss that target. So pinning down a location for an electron makes the trajectory more indefinite, indeterminate, or uncertain. If the trajectory were made more clear and then we were to try to locate that electron along an extension of the trajectory we just staked out, then we would find that the more precise we made our knowledge of the trajectory, the less likely we would be to find the electron where ordinary expectations would lead us to believe it to be.

The Planck constant (sometimes called Planck's constant), links the amount of energy a photon carries with the frequency of its electromagnetic wave. It is named after the physicist Max Planck. It is an important quantity in quantum physics.

The Planck constant is defined by the equation:

E=hv

9.Wave function. Interpretation of the Wave Function: Probability Density and Expectation Values.The probability of finding photon within a given volume of the beam is proportional to the square of the amplitude of the wave associated with this beam

In quantum mechanics, the Wave function, usually denoted by Ψ, or ψ, describes the probability of finding an electron somewhere in its matter wave. To be more precise, the square of the wave

function gives the probability of finding the location of the electron in the given area, since the normal answer for the wave function is usually a complex number. The wave function concept was first introduced in the legendary Schrödinger equation.

10.The Schrodinger equation and Schrodinger’s favorite petКартина квантовых событий, которую дает нам уравнение Шрёдингера, заключается в том, что электроны и другие элементарные частицы ведут себя подобно волнам на поверхности океана. С течением времени пик волны (соответствующий месту, в котором скорее всего будет находиться электрон) смещается в пространстве в соответствии с описывающим эту волну уравнением. То есть то, что мы традиционно считали частицей, в квантовом мире ведёт себя во многом подобно волне.

11.Tunneling through a potential energy barrier.

The phenomenon of tunneling, which has no counterpart in classical physics, is an important consequence of quantum mechanics. Consider a particle with energy E in the inner region of a one-dimensional potential well V(x). (A potential well is a potential that has a lower value in a certain region of space than in the neighbouring regions.) In classical mechanics, if E < V (the maximum height of the potential barrier), the particle remains in the well forever; if E > V , the particle escapes. In quantum mechanics, the situation is not so simple. The particle can escape even if its energy E is below the height of the barrier V , although the probability of escape is small unless E is close to V . In that case, the particle may tunnel through the potential barrier and emerge with the same energy E.

The phenomenon of tunneling has many important applications. For example, it describes a type of radioactive decay in which a nucleus emits an alpha particle (a helium nucleus). According to the quantum explanation given independently by George Gamow and by Ronald W. Gurney and Edward Condon in 1928, the alpha particle is confined before the decay by a potential. For a given nuclear species, it is possible to measure the energy E of the emitted alpha particle and the average lifetime of the nucleus before decay. The lifetime of the nucleus is a measure of the probability of tunneling through the barrier--the shorter the lifetime, the higher the probability.

12.Atomic Spectra of Gases.   Balmer’s,   Lyman’s, Paschen’s and   Brackett’s series.How do we get an Atomic Absorption Spectrum?

Light comes from a light source. That’s the bulb in the picture below. It is usually a pretty strong light source. A sample of an element, such as aluminium, chlorine etc, is vaporized. The light passes through the sample, and bits of the light are absorbed. The remainder of the light is then passed through a crystal, broken up into its component colors and then it can be analysed.

An atomic emission spectrum is the opposite of an atomic absorption spectrum. While an absorption spectrum has parts missing from the rainbow, the emission spectrum is made up only of a few lines of color. They are the SAME lines of color that would be missing in the absorption

spectrum for the same sample you test.

How do we get an emission spectrum?

The process of obtaining an emission spectrum is slightly different to that for the atomic absorption spectrum. A sample of an element or compound is made into a gas and heated. As it gets hotter, the atoms absorb the energy. When the flame is turned off and the gas is allowed to cool, the atoms release the energy as light.

Lyman series (n′ = 1)

The series is named after its discoverer, Theodore Lyman, who discovered the spectral lines from 1906–1914. All the wavelengths in the Lyman series are in the ultraviolet band.[5][6]

Balmer series (n′ = 2)

Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen.[7] Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.

Paschen series (Bohr series) (n′ = 3)

Named after the German physicist Friedrich Paschen who first observed them in 1908. The Paschen lines all lie in the infrared band.[8] This series overlap with the next (Brackett) series, i.e. the shortest line in the Brackett series has a wavelength that falls among the Paschen series. All subsequent series overlap.

Brackett series (n′ = 4)

Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922.

13.Emission and absorption spectroscopy.14.Total energy of the atom. Formula’s derivation.15.Bohr radius.

The Bohr radius is a unit of measurement used in atomic physics to describe the smallest possible radius of an electron orbiting the nucleus in a hydrogen atom. It was developed by Niels Bohr, based on his model of atomic structure, which was introduced in 1913. The value of the Bohr radius is calculated to be approximately 0.53 angstroms.

In his model of an atom, Niels Bohr theorized that electrons follow specific circular orbits

around the central nucleus, held in place by electrostatic force. This model later proved to be incorrect and is now considered far too simple a description of atomic structure. Current theories describe the location of electrons in terms of spherical probability zones, known as shells. The Bohr radius is still considered useful in physics, however, as it continues to provide a physical measurement for the smallest radius an electron can have. Physics students often learn Bohr’s model and equations first, as an introduction before moving on to more complicated and accurate models.

Hydrogen, with only one electron, is the simplest of all atoms, which is why the Bohr radius is based on it. Bohr’s model explains that the orbit of an electron can vary depending on the amount of energy it has. The Bohr radius estimates the orbit of the hydrogen electron while it is in its ground state, or at lowest energy.

16.Thomson and Rutherford models of Atom.

By 1911 the components of the atom had been discovered. The atom consisted of subatomic particles called protons and electrons. However, it was not clear how these protons and electrons were arranged within the atom. J.J. Thomson suggested the"plum pudding" model. In this model the electrons and protons are uniformly mixed throughout the atom:

Rutherford tested Thomson's hypothesis by devising his "gold foil" experiment. Rutherford reasoned that if Thomson's model was correct then the mass of the atom was spread out throughout the atom. Then, if he shot high velocity alpha particles (helium nuclei) at an atom then there would be very little to deflect the alpha particles. He decided to test this with a thin film of gold atoms. As expected, most alpha particles went right through the gold foil but to his amazement a few alpha particles rebounded almost directly backwards.

These deflections were not consistent with Thomson's model. Rutherford was forced to discard the Plum Pudding model and reasoned that the only way the alpha particles could be deflected backwards was if most of the mass in an atom was concentrated in a nucleus. He thus developed the planetary model of the atom which put all the protons in the nucleus and the electrons orbited around the nucleus like planets around the sun.

17.Bohr’s Model of the Hydrogen Atom.

Overview of the Bohr Model

Niels Bohr proposed the Bohr Model of the Atom in 1915. Because the Bohr Model is a

modification of the earlier Rutherford Model, some people call Bohr's Model the Rutherford-Bohr Model. The modern model of the atom is based on quantum mechanics. The Bohr Model contains some errors, but it is important because it describes most of the accepted features of atomic theory without all of the high-level math of the modern version. Unlike earlier models, the Bohr Model explains the Rydberg formula for the spectral emission lines of atomic hydrogen.The Bohr Model is a planetary model in which the negatively-charged electrons orbit a small, positively-charged nucleus similar to the planets orbiting the Sun (except that the orbits are not planar). The gravitational force of the solar system is mathematically akin to the Coulomb (electrical) force between the positively-charged nucleus and the negatively-charged electrons.

Main Points of the Bohr Model

Electrons orbit the nucleus in orbits that have a set size and energy.The energy of the orbit is related to its size. The lowest energy is found in the smallest orbit.Radiation is absorbed or emitted when an electron moves from one orbit to another.Bohr Model of Hydrogen

The simplest example of the Bohr Model is for the hydrogen atom (Z = 1) or for a hydrogen-like ion (Z > 1), in which a negatively-charged electron orbits a small positively-charged nucleus. Electromagnetic energy will be absorbed or emitted if an electron moves from one orbit to another. Only certain electron orbits are permitted. The radius of the possible orbits increases as n2, where n is the principal quantum number. The 3 → 2 transition produces the first line of the Balmer series. For hydrogen (Z = 1) this produces a photon having wavelength 656 nm (red light).

18.The Quantum Model of the Hydrogen Atom. Electron cloud. Atomic orbital.

The electron cloud model is an atom model wherein electrons are no longer depicted as particles moving around the nucleus in a fixed orbit. Instead, as a quantum mechanically-influenced model, we shouldn’t know exactly where they are, and hence describe their probable location around the nucleus only as an arbitrary ‘cloud’.

19.Physical Interpretation of the Quantum Numbers.

Quantum Numbers Quantum numbers are required to describe the distribution of electron density in an atom. There are three quantum numbers necessary to describe an atomic orbital.

The principal quantum number (n) – designates size The angular moment quantum number (l) – describes shape The magnetic quantum number (ml) – specifies orientation

The electron spin quantum number (ms ) is used to specify an electron’s spin. There are two possible directions of spin (направления вращения) . Allowed values of ms are +½ and −½. (clockwise or counterclockwise).

20.The Exclusion Principle and the Periodic Table

The Pauli exclusion principle refers to the fact that certain particles cannot be at the same place at the same time, with the same energy. Only fermions (examples are protons, neutrons and electrons) are bound by the Pauli exclusion principle, while bosons (an example is a photon - light beam) are not. A more precise way to describe the Pauli exclusion principle is to say that two of the same kind of fermions cannot have the same quantum numbers.

No two electrons can ever be in the same quantum state; therefore, no two electrons in the same atom can have the same set of quantum numbers.

The periodic table of the chemical elements is a list of known atoms. In the table, the elements are placed in the order of their atomic numbers starting with the lowest number. The atomic number of an element is the same as the number of electrons or protons in that particular atom.21.Spontaneous and stimulated emission. Lasers.

light amplification by stimulated emission of radiation"

• Laser light is coherent. The individual rays of light in a laser beam maintain a fixed phase relationship with one another. • Laser light is monochromatic. Light in a laser beam has a very narrow range of wavelengths. • Laser light has a small angle of divergence. The beam spreads out very little, even over large distances.

22.Atomic bonding. 

 Primary bonding involves transfer or sharing of electrons and produces a relatively strong joining of adjacent atoms. Example: ionic, covalent and metallic bonds. Secondary bonding involves a relatively weak attraction between atoms in which no electron transfer or sharing occurs. Example: Van-der-Waals bonds are in this category.23.Properties of nuclei. Isotopes.Some Properties of NucleiComposition Size Mass

Size - how big is a nucleus?On the basis of many scattering experiments, it is found that most nuclei are approximately spherical and have an average radius given by: r = r0A1 3 where A is the mass number and r0 is a constant equal to 1.2 x 10-15 m

Composition:All nuclei appear to contain two kinds of particles bound together. These are protons and neutrons.Protons have a charge of +e.Neutrons are neutralThe atomic number, Z, of a nucleus is just the number of protons that it contains. This is sometimes called the charge number.The neutron number, N, is the number of neutrons.The mass number, A, is equal to the total number of particles, neutrons and protons, present in the nucleus: A = Z + N.

liquid drop model

The atoms of a chemical element can exist in different types. These are called isotopes. They have the same number of protons (and electrons), but different numbers of neutrons. Different isotopes of the same element have different masses. Mass is the word for how much substance (or matter) something has. Things with different masses have different weights. Because different isotopes have different numbers of neutrons, they do not all weigh the same or have the same mass.

Different isotopes of the same element have the same atomic number. They have the same number of protons. The atomic number is decided by the number of protons. Isotopes have different mass numbers, though, because they have different numbers of neutrons.

The word isotope, meaning at the same place, comes from the fact that isotopes are at the same place on the periodic table.

In a neutral atom, the number of electrons equals the number of protons. Isotopes of the same element also have the same number of electrons and the electronic structure. Because how an atom acts is decided by its electronic structure, isotopes are almost the same chemically, but different physically to their original atoms.

Heavier isotopes react slower than lighter isotopes of the same element. This "mass effect" is

large for protium (1H) and deuterium (2H), because deuterium has twice the mass of protium. For heavier elements, the relative atomic weight difference between isotopes is much less, and the mass effect is usually small.

24.Radioactivity. Decay processes.

Radiation is when energy moves through space away from a source (of radiation). There are two broad classes of radiation: ionizing radiation which comes from radioactive materials and x-ray machines and non-ionizing radiation (usually electromagnetic radiation) which comes from other sources. Ionizing radiation, which carries a large energy in each particle, can change things that it hits, hurting people or animals or causing chemical changes. Non-ionizing radiation does not cause microscopic damage, but some types can cause chemical changes or make things hotter.

There are many different ways that energy can travel through space in this way. One way is in the form of shifting electrical and magnetic fields. This is why some common types of radiation are referred to as Electromagnetic radiation, also known as light. (A different way to think of electromagnetic radiation is as a stream of particles of energy called photons.) Another way that radiation can travel is in the form of tiny particles. These are pieces of atoms, like neutrons or protons (please see the article on atoms for more information). When radiation is made up of quickly moving particles (like pieces of atoms), it is referred to as particle radiation.

Most people hear terms like radiation and immediately think of it as a bad or dangerous thing. It turns out that only certain types of radiation are ordinarily harmful to humans. For example, ultraviolet radiation can give people sunburns. X-rays and gamma rays can make a person sick, or even die if they are exposed to them for a very long time. Some types of particle radiation can also make people sick and lead to burns. Any type of radiation that causes changes in the world like these is referred to as ionizing radiation.

Most chemical elements are stable: If they are not part of a chemical reaction, they do not change. Chemical elements are made of atoms. In stable elements, the atom stays the same. In a chemical reaction, the atoms will form chemical bonds, with other atoms. Even if the bonds change during a reaction, the atoms themselves do not.

Radioactive decay changes an atom from one that has higher energy inside its nucleus into one with lower energy. The change of energy of the nucleus is given to the particles that are created. The energy released by radioactive decay may either be carried away by a gamma ray electromagnetic radiation (a type of light), a beta particle or an alpha particle. In all those cases, the change of energy of the nucleus is carried away. And in all those cases, the total number of positive and negative charges of the atom's protons and electrons sum to zero before and after the change.

The speed at which this change happens, is different for each element. Radioactive decay is governed by chance: The time it takes, on average for half the atoms of a substance to change is called half-life. As an example, iodine (131I) has a half-life of about 8 days. That of plutonium ranges between 4 hours (243Pu) and 80 million years[4] (244Pu)

25.Superconductivity.Superconductivity is a phenomenon in which some materials lose all electrical resistance at very low temperatures. For example if Lead is gradually cooled its resistance steadily decreases (this

is common for most conductors). But if cooled below 7.2 degrees Kelvin its resistance suddenly drops to zero. In this state a ring made of lead is able to conduct a current that cycles for years (creating magnetic fields) without any observed decay.

A current moving forever in a loop is a seeming impossibility. It breaks the rules of electrical resistance, physical friction and thermodynamics; all of which would predict some sort of energy loss. After all, even if the loop were made of the best non-superconducting conductors available the current would rapidly dissipate.

What is a superconductor, anyway? A superconductor is a material with zero electrical resistance. That is, when you send a current into it, that current flows straight through it as if it weren’t there. Better yet, you get persistent currents– if you start a current flowing in a loop of superconductor, it will keep flowing forever, unlike a normal conductor, where losses to heat and so on will cause the current to dissipate pretty quickly unless you do something to keep it going.

That sounds pretty awesome. Useful, too. So, how does it work? It took a while to figure out what’s going on, but one of the key bits of information is that the transition from a normal material to a superconductor happens abruptly, at very low temperature. This suggests that it might somehow be associated with another weird phenomenon that happens at extremely low temperatures, Bose-Einstein Condensation.

The way to do this is to pair the electrons up. The characteristic spin behavior of electrons is what makes them unable to occupy the same quantum state in large numbers, but if you put two electrons together in the right way, you can make a composite particle with either no spin at all (one electron spin-up, the other spin-down), or a spin of 1 (both up or both down). That composite particle is a boson, so you can make a BEC of electron pairs, and use that to explain superconductivity.

OK, but how do you stick two electrons together to make a boson? They repel each other, don’t they? Two isolated electrons do repel each other, but two electrons in a superconductor aren’t isolated– they’re in the middle of a huge lattice of positively charged atoms making up the solid.

And that’s the key. Two electrons by themselves can’t be stuck together, but two electrons inside a lattice can develop an attractive force between them that’s mediated by the lattice.

the Cooper pairing mechanism depends on displacements of atoms in the lattice due to the passing electrons. At high temperatures, though, the atoms in the lattice are moving all over the place all on their own– the temperature, you remember, is a measure of the energy of the atoms making up a substance. High-temperature materials have their atoms vibrating by too much for the tiny tug of a passing electron to create a significant effect. In order for Cooper pairing to work, the solid needs to be cold enough that the tiny additional motion caused by a passing electron is large compared to the thermal vibrations.