anomalous diffraction

An approach to solving the phase problem in protein structure determination by comparing structure factors collected at different wavelengths, including the absorption edge of a heavy-atom scatterer. Also known as multiple-wavelength anomalous diffraction or multiwavelength anomalous dispersion.

The 'normal' atomic scattering factor f0 describes the strength of X-rays scattered from the electrons in an atom assuming that they are free oscillators. Because the scattering electrons are in fact bound in atomic orbitals, they act instead as a set of damped oscillators with resonant frequencies matched to the absorption frequencies of the electron shells. The total atomic scattering factor f is then a complex number, and is represented by the sum of the normal factor and real and imaginary 'anomalous' components:
f = f0 + f' + if''.

A consequence of the wavelength dependence of anomalous dispersion is that the structure factors will be significantly perturbed, both in amplitude and in phase, by resonant scattering off an absorption edge. Hence, if diffraction is carried out at a wavelength matching the absorption edge of a scattering atom, and again at a wavelength away from the absorption edge, comparison of the resulting diffraction patterns will allow information to be extracted about the phase differences. For suitable species, the effect is of comparing a native molecule with a strictly isomorphous derivative (and in such cases phase determination and improvement are similar to isomorphous replacement methods).

The technique, often using tunable synchrotron radiation, is particularly well suited to proteins where methionine residues can be readily replaced by selenomethionine derivatives; selenium has a sufficiently strong anomalous scattering effect that it allows phasing of a macromolecule.
The method of Multiple wavelength Anomalous Diffraction (MAD) is most applicable to problems where there are no available separate native protein diffraction data, e.g. for metallo-proteins where a heavy atom is already bound in the native structure, or to cases where derivative crystals are non-isomorphous and are therefore unsuitable for phasing via isomorphous replacement.

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Diffraction grating

Introduction :
In optics, a diffraction grating is an optical part with a periodic structure, which splits and diffraction light into some beams travelling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the brightness so that the grading acts as dispersive element. Because of this, diffraction gradings are generally used in monochromators and spectrometers.

Diffraction grating definition

A photographic slide with a well model of black lines forms a simple grating. For useful applications, diffraction gradings usually have grooves or rulings on their outside rather than dark lines. Such gradings can be moreover transparent or reflective. Gratings which change the phase rather than amplitude of the incident light are also formed, frequently using holography.
                                            (Source : Wikipedia)

Theory of operation

The connection between the grading spacing and the angles of the event and diffracted beams of light is known as the grating equation. According to the Huygens–Fresnel standard, each point on the wave front of a propagating signal can be measured to act as a point source, and the wave front at any following point can be found by calculation together the contributions from every of these individual position sources.
                                                              (Source :Wikipedia)
An idealized diffraction grating is measured here which is made up of a position of long and considerably narrow slits of spacing d. When a level surface signal of wavelength λ is incidence usually on the grating, each slit in the grading acts as a point source propagate in all directions. The light in a exacting direction, θ, is made up of the interfering components from each slit.This occurs at angles θ_m which satisfy the connection dsinθ_m/λ=|m| where d is the division of the slits and m is a digit. Thus, the diffracted light will have maxima at angles θ_m given by

It is basic to show that if a plane wave is event at an angle θ_i, the grating equation becomes

Gratings can be made in which a mixture of the incident light are modulate in a regular example

• Transparency (transmission amplitude gratings)
• Reflectance (reflection amplitude gratings)

• Refractive index (phase gratings)
• Direction of optical axis (optical axis gratings)

The grating equation applies in all these cases.a


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Uses of Carbon Compounds

 The study of carbon compounds is called organic compounds.Carbon compounds are covalent compounds having low melting points and boiling point. It shows that forces of attraction between their molecules are not very strong. Most of the carbon compounds are non-conductors of electricity. They do not contain ions. Carbon compounds occur in all living things like plants and animals. The number of carbon compounds already known at present is more than 5 million. Many more new carbon compounds are being isolated or prepared in the laboratories everyday. In fact, the number of carbon compounds alone is much more than the number of compound is all other elements taken together. One reason for the existence of a large number of carbon compounds is that carbon atoms can link with one another by means of covalent bonds to form long chains of carbon atoms. This property is called Catenation. Carbon-carbon bonds are strong, and stable. This property allows carbon to form an almost infinite number of compounds; in fact, there are more known carbon-containing compounds than all the compounds of the other chemical elements combined except those of hydrogen.

Uses of Carbon Compounds.

The compounds of carbon with hydrogen are called hydrogen. In addition to hydrogen, carbon compounds may also contain other elements such as oxygen, halogens nitrogen and sulfur. This increases the number of carbon compounds even further. Today, millions of carbon compounds containing a variety of other elements are in our daily life. For example, we use soap for taking bath and detergent powders for washing clothes. The soaps and detergent which are used as cleansing agents in our daily life are carbon compounds. In fact, carbon compounds are being used on our everyday life in the form of medicines, plastics, textiles, dyes, food preservatives, soaps and detergents, sources of energy and many other things.

Stability of Carbon dioxide

Introduction : 

A Scottish chemist and physician JOSEPH BLACK discovered Carbon Dioxide, in 1754. Carbon Dioxide is very popular in Green house effect produced due to human activities, primarily by the combustion of fossil fuels. Carbon Dioxide can be easily found in the earth’s atmosphere, as the main source of carbon dioxide is humans and plants.

About Carbon Dioxide

Carbon Dioxide is a chemical compound composing of two oxygen atoms, which are covalently bonded to the single carbon atom.The chemical formula of carbon dioxide, is CO_2. Carbon dioxide generally exists as gas at room temperature. Carbon Dioxide forms 0.039% of the atmospheric air. Carbon dioxide is also present in liquid and solid forms under some special conditions. It can be solid when temperature will be as low as -78 ⁰C. Liquid carbon dioxide mainly exists when it is dissolved in water. Carbon dioxide is one of the gases, which is easily dissolved in water, when pressure is maintained. Carbon dioxide on leaving water gives bubbles

Properties of carbon Dioxide and its Stability

Carbon dioxide can be found mainly in air, but also in water because of carbon cycle. Some of the important properties of Carbon dioxide are as follows:

• Plants use it during the photosynthesis to make sugars, which will be consumed by them for their essential growth and development.
• It is generated as a byproduct in the combustion of fossil fuels and in the burning of vegetable matter.
• Amount of CO₂ present in the atmosphere changes due to the effect of plant growth.
• CO₂ has no liquid state below 5.1 atm pressure.
• In its solid-state carbon dioxide is known as Dry Ice.
• CO₂ is an acidic oxide; as a result, it turns litmus from blue to pink.
• CO₂ is an anhydride of Carbonic acid.
• CO₂ is toxic in higher concentrations, as a result it make people drowsy
• CO₂ is a colorless and odorless gas having acidic odor.
• It acts as an asphyxiant and an irritant.

The main reason for the stability of carbon dioxide in atmosphere is the carbon cycle, in which human, animals exhale carbon dioxide, and this CO₂ is being taken by plants during day to prepare their food essential for their growth, while in night plants also produce carbon dioxide. This entire process makes the carbon dioxide stable in the atmosphere.

Summary on Stability of Carbon dioxide

Carbon Dioxide is an organic compound used widely in commercial purposes. As it is used in the production of lasers and even in the soft drinks. This compound exists naturally in the earth's environment. Scientists became concerned by the fact that humans are producing too much carbon dioxide for plants to process, if it will continue to follow then it will lead to serious environmental problems.

Thermal conduction

Heat can be transferred from one place to another by three different methods, namely Conduction, Convection and radiation. Conduction usually takes place in solids, Convection in fluids (liquids and gasses), and no medium is required for radiation.

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Conduction is a mode of heat transfer between two neighboring molecule due to the difference in temperature. It occurs in all forms of matter (solids, liquid and gas).Ex. - conduction of heat through metals

Convection is a mode of heat transfer due to the actual movement of molecule and it occurs in fluids only .E g.: - wind is convectional mode of heat transfer

Radiation is a mode of heat transfer which requires no medium for the heat transfer. E.g. sun radiates heat.  

Thermal conduction
Conduction

Conduction is the process in which heat is transmitted from one point to another through the substance without the actual motion of the particles. When one end of a metal bar is heated, the molecules at the hot end vibrate with higher amplitude and transmit the heat energy from one particle to the next particle. However, the particles remain in their mean position of equilibrium. The process of conduction is prominent in the case of solids.

If one end of a metal rod is placed in a stove, the temperature of the other end gradually increases. Here heat is transferred from one end to the other end due to the molecular collisions and the process is called heat (thermal) conduction. Here the average position of a molecule does not change and hence, there is no mass movement of matter.

The ability of a material to conduct heat is measured by thermal conductivity of the material. If ΔQ amount of heat crosses through any cross- section in time Δt, ΔQ/ Δt is called the heat current. It is found that in steady state it is proportional to the area of cross section A, proportional to temperature difference(T1-T2) between the ends and inversely proportional to the length x . Thus,

ΔQ/ Δt ~ A (T1- T2) / x                                                                   ΔQ/ Δt = K A (T1- T2) / x

                                                                                                             Here K is a constant for the material of the slab and is called the thermal conductivity of the material.

In general, solids are better conductors than liquids and liquids are better conductors than gases. Metals are better conductors than non-metals. This is because; in metals we have a large number of 'free electrons' which can move freely any where in the body of the metal. These free electrons help in carrying the thermal energy from one place to another in a metal. 

Convection

Convection

In convection heat is transferred from one place to another by actual motion of heated material. The process of convection is prominent in the case of liquids and gases. Land and sea breezes and trade winds are formed due to convection. Convection plays an important role in ventilation, gas filled electric lamps and heating of buildings by hot water circulation.

In a hot air blower, air is heated by a heating element and is blown by a fan. The air carries the heat wherever it goes. If the material moves due to the difference in density, it is called natural or free convection.

             The main mechanism for heat transfer inside a human body is forced convection.  Heat serves as the pump and blood as the circulating fluid. Heat is lost to the atmosphere through all the three processes conduction, convection and radiation. The rate of loss depend on clothing, the tiredness, air current, humidity  and several other factors. The system, however, transports the just required amount of heat and hence maintains a remarkably constant body temperature.

Radiation

Radiation

The process of radiation doesn’t need a material medium for heat transfer. Energy is emitted by a body and this energy travels in the space just like light. When it falls on a material body, a part is absorbed and the thermal energy of the receiving body is increased .The energy emitted by a body in this way is called radiant energy, thermal radiation or simply radiation .The heat from the sun reaches the earth by this process , traveling millions of kilometers of empty space.

Electrochemical cell

Introduction :
Electrochemical is the learning of production of electricity from energy released during the spontaneous chemical reaction and the use of electrical energy to bring about non spontaneous chemical transformation. Important equally of the abstract and useful consideration. A large number of metal, sodium hydroxide, chlorine, fluorine and many other chemical are produce by electrochemical methods. Batteries and fuel cells converted chemical energy into electrical energy and are used to a large scale in various instrument and devices.

Daniel cell of electrochemical cells:

An electrochemical cell is used to convert the electrical energy to the chemical energy.We had studied the construction and functioning of Daniell cell. This group converts the chemical energy unconventional through the redox reaction.
Zn(s) +Cu²⁺ (aq)   `harr`  zn²⁺ (aq) +Cu(s)
 
To electrical energy and has an electrical potential equal to 1.1 V when concentration of Zn2+ and Cu2+ ions is unity such a device is called a galvanic or voltaic cell. If an internal opposite potential is applied in the galvanic cell and decreased slowly, we find that the reaction continues to take place till the operating voltage reaches stops altogher and no current flows through the cell.
                Any additional enlarge in the external possible gain again create the response but in the opposite direction. It now functions as an electrolytic cell, tool for using electrical energy to carrying non spontaneous chemical reaction. Equally types of cell are given up significant and we shall study some of their salient feature in the following pages.

Classification of the electrochemical cell:

Oxidation-reduction or redox reactions obtain position in electrochemical cells. Generally two classifications of electrochemical cells. Spontaneous reactions occur in galvanic (voltaic) cells; no unstructured reactions occur in electrolytic cells. Both types of cells include electrodes where the oxidation and decrease reactions occur. Oxidation occurs at the electrode term the anode and decrease occur at the electrode call as cathode.
             A possible difference develops among the electrode and the electrolyte which is call electrode potential. When the concentration of each the class implicated in a partly cell is combination then the electrode potential is well-known as standard electrode potential.

Harmonic oscillator phase

In classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:
where k is a positive constant.

If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:
Oscillate with a frequency smaller than in the non-damped case, and an amplitude decreasing with time (underdamped oscillator). Decay exponentially to the equilibrium position, without oscillations (overdamped oscillator).

If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator.Mechanical examples include pendula (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves.

Simple harmonic oscillator

A simple harmonic oscillator is an oscillator that is neither driven nor damped. Its motion is periodic— repeating itself in a sinusoidal fashion with constant amplitude, A. Simple harmonic motion SHM can serve as a mathematical model of a variety of motions, such as a pendulum with small amplitudes and a mass on a spring. It also provides the basis of the characterization of more complicated motions through the techniques of Fourier analysis.

In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period T, the time for a single oscillation, its frequency, f, the reciprocal of the period f = 1⁄T (i.e. the number of cycles per unit time), and its phase, φ, which determines the starting point on the sine wave. The period and frequency are constants determined by the overall system, while the amplitude and phase are determined by the initial conditions (position and velocity) of that system. Overall then, the equation describing simple harmonic motion.