Atomic and ionic radii

Introduction :

Atomic radii are also known as covalent radius.  Atomic radii describes the size of the atom of an element in its elementary state or in covalently linked molecule. It is measured in terms of picometers or Angstroms. It is the distance from the nucleus to the boundary of the surrounding cluster of electrons.

The bond length of a covalent linkage is the distance between the nuclei of the two bonded atoms. The bond length can be measured by X-diffraction method.

The internuclear distance between two unlike atoms in a covalent bond is the sum of the atomic radii of the two. For example, the covalent radii of hydrogen and chlorine are 0.037 nm and 0.099 nm respectively. Hence the internuclear distance in HCl molecule is 0.037 nm + 0.099 nm = 0.136 nm.

The atomic size will generally decrease from left to right in a period. This is because, when we proceed from one element another in a period, this results in a greater pull on electrons towards the nucleus. In a given period, the alkali metal atom of group 1A is the largest and the halogen atom in 7A is the smallest.

Ionic radii:

The ionic radii may be defined as the distance between the nucleus of an ion and the point up to which the nucleus has influence on its electron cloud.
The concept of ionic radii was developed independently by Victor Goldschmidt and Linus Pauling in 1920.
If ions in a crystal are regarded as spheres, the internuclear distance between two ions is equal to the sum of the radii of the ions. The internuclear distance is measured by X-ray analysis of ionic compounds. Knowing the radius of one ion, that of the other is calculated.
The interionic distance in potassium chloride crystal is 0.314 nm= r K⁺ + r Cl^- = 0.314 nm where r K⁺ and r Cl^- are the radii of potassium ion and chloride ion respectively. It is found that r K⁺ = 0.314 nm   Therefore r Cl^- = 0.314-0.133 = 0.181 nm.

Atomic scale

Introduction:- Many chemical phenomena occur around us and these are explained on the basis that matter is made up of molecules. Molecules,in turn, are made up of atoms. daltons atomic theory  that an atom is an indivisible particle.  but reaserch findings of the last hundred years on the study of gases in particular and then of solids,led to the discovery of the fundamental particles,viz., electron,proton and nutron. various atomic models  to indicte the arrangement of these fundamental particles in an atom were proposed. an atom consists of a nucleus at its center. protons and nutrons are present  in the nucleous while electrons revolve aroud the nucleous. the charges and masses of  the fundemental particles are listed below.  
         It is especially focus on the properties. There are two kinds of atomic units.

1. Hartree atomic units.
2.  Rydberg  atomic units.   The numerical values of the follwing four fundemental physical constants are all units by definition                                                             electron mass                                                                                                                                                                                                                       elementary charge                                                                                                                                                                                                              reduced plank's constant                                                                                                                                                                                                    columbs constant.

Atomic number:-

 Every atom of a given element consists of a definite number of electrons. this number is called the atomic number of the element. it is denoted by Z.Moseley proposed that a simple relation between the frequencies of the charecteristic X-rays given by element and its atomic number.When a meterial target,called anticathode,is placed in the path of cathode rays in a discharge tube,X-rays charecteristic of the metal are emitted from the metal target.

MASS NUMBER:-

 The total of the numer of protons and nutrons present in an atom  is reffrred to as the mass number(A) of the atom of that element.This is mathematically written as
                                              A=Z+N.
                                where Z is the atomic number and N is the number of nutrons.Hence mass number is always positive.Atoms ofan element which differ in their mass but have the same atomic number are  called isotopes of that element.The isotopes of an element thus have the same number of protons but differ in the number of nutrons present in them.

Fundamental atomic units 

Fundamental Atomic Units
Dimension	Name	Symbol	Value in SI units
mass	electron rest mass	me	9.1093826(16)×10−31 kg
charge	elementary charge	e	1.60217653(14)×10−19 C
angular momentum	Reduced Planck's constant	h-=h/2π	1.05457168(18)×10−34 J·s
electric constant	Coulomb force constant	1 / (4πε0)	8.9875517873681×109 kg·m3·s-2·C-2

Atomic models:-

Rutherford model:-
                                  
Rutherfords experiment showed that most of the space in an atom is empty and all the mass of the atom and its positive charge are concentrated at the center of   the atom which is spherical in shape.The center point of the positive charge is called "atomic nucleus". The electrons revolve round the nucleus in circular orbits just as planets revolve round the sun.
This model failes to explain two important facts:

• As per the law of electrodynamics ,a charged particle like electron in circular motion around the opposite charge should continously lose energy by emission and spiral down into the nucleus due to nucleus attraction.If this happens ,the atom should collaps which is not happening.

If the electron in an atom continuosly radiates energy ,the spectrom of that element should be continous spectrom.But the eseatoms give rise to discontinuous line specta with we defined lines.        

Neon atomic symbol

Introduction to Neon:

Neon's discovery happened in 1898 by Ramsay & Travers. It is one of the rarest gases present in atmosphere to the extent of 1 part in 65,000 in the air. It is first obtained by air liquefaction and then through fractional distillation for separation of other gases. It is part of Group 18 elements in periodic table.

Properties and application of Neon:

Neon is a compound mixture of 3 isotopes. Apart from this, there are six other unstable isotopes. Though Neon is an inert element, it is found to have produced a compound in reaction with fluorine. Some of the ions of Neon are used in the study of mass spectroscopy and optical spectroscopy. It is used as a refrigeration compound in place of Helium as it costs less. At normal conditions of voltage & current, Neon displays intense behavior compared to all other inert gases.

Neon has an Atomic Mass of 20.1797 amu. Its melting point is supposed to be -248 °C.  Its boiling point is considered-246 °C.  Its crystal structure is in the form of a face-centered cube. Its density is supposed to be 0.9002 g/cm3

Neon is used in signboards as it appears very bright and reddish orange in color. Neon lights are used during foggy seasons as it can penetrate fog.  It is used in vacuum tubes, television tubes and in lasers. Liquid neon is used as a cryogenic refrigerant. But liquid neon is very expensive compared to liquid helium.

Neon belongs to p-block of noble gases in the periodic table. It is supposed to be the most inert element. It is believed by scientists that neon reacts with fluorine to produce different compounds. On reaction with water, neon produces unstable hydrate. Neon is produced in huge quantities during volcanic eruptions.  It combines with helium  gas to produce neon-helium lasers.

Conclusion:

Neon being the fifth most abundant element has variety of applications. It is also the second lightest gas and inert in nature which helps us in various applications.

Atomic structure protons

Introduction 
It is very essential to know the composition of matter to determine both of its physical and chemical properties. Atomic theory is a theory of the nature of matter. The composition of  matter is discrete units called atoms, as opposed to the notion that matter could be broken into any arbitrarily small quantity. It began in ancient Greece and India as Philosophical science and the field of chemistry showed that matter indeed behaves as if it is made up of particles.
John Dalton, in 1808 proposed a theory in which he stated that matter consists of very small indivisible particles called atoms. The word "atom" (Greek adjective atomos = uncut, 'indivisible’) was applied to the basic particles. The atomic structure itself was imagined to be the indivisible particle. However, around the 20th century, through various experiments with electromagnetism and radioactivity, physicists discovered that the atomic structure is actually an aggregate of various subatomic particles.  Since atoms were found to be divisible, physicists introduced the term "elementary particles" to describe indivisible particles. This field of science was believed to be the basis to discover the true fundamental nature of matter.

Fundamental particles – Constituents of atoms

J J Thomson studied the conduction of electricity by gases at low pressure. A kind of negatively charged particles were found to be emitted by the cathode. These were called ‘cathode rays’. The properties of these particles were identical for all gases.  This indicated that these particles existed in all substances.  These particles were called ‘electrons’ and are represented as e^—.
The ratio of charge (e) of the electron to its mass (m) was found to be 1.76x 10¹¹ coulomb per kilogram. Since an atomic structure is neutral, it should contain as much positive charge as negative charges carried by all electrons.
The lightest atom known is the hydrogen atom. It contains an electron and a positively charged particle. The positively charged particle obtained by removing the electron from a hydrogen atom was called a proton. It is represented as ₁p¹.
Mass of a proton is found to be 1.672 x 10^-27 kg.
Its charge is +1.602 x 10^-19C.
In 1932, James Chadwick discovered a new particle called a ‘neutron’, when he bombarded a thin beryllium foil with alpha (α) particles.  The electrons, protons and neutrons are the fundamental particles present in atomic structure.

Particle	Mass		Charge Unit = 1.602x10-19C
	kg	a.m.u
Electron	9.109x10-31	0.0005486	-1
Proton	1.672x10-27	1.007277	+1
Neutron	1.675x10-27	1.008665	0

Atomic Number vs Atomic Mass

After the discovery of the neutrons, it has been established that the nucleus contains two types of particles namely protons and neutrons. The protons are responsible for the positive charge of the nucleus.
The number of protons present in the nucleus of an atom is known as atomic number (Z) of the element.  However, as the atomic structure is neutral in nature, it should contain an equal number of positive charges and negative charges. Hence, atomic number is also equal to the number of electrons present in the atom of the element.
The sum of the number of protons and neutrons present in the nucleus of the atom is called mass number (A).  The protons and neutrons are called ‘nucleons’.
Thus, Z = atomic number = no. of protons.
         A = mass number  =   no. of protons + no. of neutrons
        Therefore, A-Z = no. of neutrons.

Light diffraction pattern

 Light is a wave.  It is the fact that light is a wave that causes it to make a diffraction pattern.  The best way to understand why this works is to do a similar experiment with water in a bathtub.  First side with a small gap in between.  The idea is to block water from moving from one side of the tub to the other, except via the small gap, which should be a couple of inches wide.  Plywood also works great.  Then you can tap the surface of the water with one hand to create waves.  You can also try gently sloshing your hand back and forth.  As the waves go through the opening in the wood, they will create exactly the same types of patterns that light does.  The only difference is that the water will have a wavelength of a few centimeters, whereas light has a wavelength of only a half of a thousandth of a thousandth of a meter (really small!)

Light diffraction pattern

If you tap the water faster, you will see that the wavelength of the water is shorter. If you tap the water slowly, then you will see that the wavelength of the water is longer. Then, what you do is you look at the water pattern that bounces back from the far end of the bathtub. You will see diffraction pattern. It won't glow like light does, but it will have a similar kind of shape, at least until the water bounces around the tub a few times and the waves get confused.
If you do this experiment for a bit, you will notice that the opening is spreading the wave out. But the pattern that is generated depends not only on how the wave is spread out, but also the shape the wave had before it spread. This is because the pattern is caused by some parts of the wave interfering with other parts. That is, at one point the wave is higher than the other. When those two parts touch, then the wave disappears. But when two high points touch, they make a very high point.
 

Fresnel diffraction pattern

Introduction :
Diffraction in the case of waves refers to their bending round the obstacles. The diffraction phenomena is more predominant when the size of he obstacle is small and is comparable with the wavelength of he incident light.

Fresnel diffraction:  In this approach source of light, the obstacle and the screen are relatively close and are at finite distances. The waves are spherical or cylindrical. The wave fronts that reach the obstacle and proceed on to illuminate the screen at any point on it are not plane ones; i.e., the rays involved are not parallel. Therefore Fresnel type of investigation of diffraction is a general one. No lenses are required to observe the diffraction pattern.
Spherical or cylindrical wave fronts are divided into large number of zones, the wavelets emanating from which superimpose to yield the intensity distribution on the screen. The amplitudes and relative phases of all the zones are taken into account to calculate the intensity distribution. So, mathematical treatment for  Fresnel diffraction is  quite complicated.

Fresnel Zones

In the above figure , S is a point source. It ends spherical wavefront in forward direction . Let the radius of the spherical wave front be 'a' after time 't'. The effect of this wavefront at P is determined by dividing the wavefront into annular or ring  shaped zones. The distances from the edges of two successive zones to point P differ by    `(lambda)/(2)`  . The annular zones having this property are known as Fresnel zones. The distance of the zeroth zone from point P is b₀ .
The first zone is at a distance       b₁    =    b₀    +    `(lambda)/(2)`.
The second zone is at a distance  b₂   =   b₀   +    `(2lambda)/(2)` 
The third zone is at a distance        b₃    =    b₀  +  `(3lambda)/(2)`
The m^th  zone is at a distance         b_m  =  b₀  +   `(mlambda)/(2)`

Conclusion to fresnel diffraction pattern:

These zones are also known as half period zones as the path difference of  `(lambda)/(2)`   corresponds to a phase difference of 180⁰  which in turn corresponds to half a period. The areas of Fresnel zones are approximately the same when m in not too great and hence an equal quantity of light energy will be transmitted through each of the zones.

edge diffraction

"Effectively, what is happening is the measurement circumstance is changing from free-field (4-pi) to half-space (2-pi) as the frequency increases and the wavelength decreases to something approaching the overall area of the baffle. This creates a response ‘step’ of about 6 dB, the frequency of the step being dependent upon the baffle area. The effect is most pronounced on-axis, as the baffle causes a beaming phenomenon like a [sic] -automobile headlight reflector."

While what is said is mostly correct, it does make one wonder:
    * How does the wave know how large the baffle is?
    * Why 6 dB?
    * Are there any other effects?
    * Are two baffles equivalent if they have the same area but vastly different dimensions, e.g. a 30 cm X 30 cm baffle vs. a 5 cm X 180 cm baffle?
In my opinion, the key to developing an intuitive or quantitative understanding of cabinet edge diffraction is by studying it primarily the time domain and resorting to the frequency domain only when absolutely necessary. Once the effect is understood in the time domain, it is easily translated to the frequency domain by using the Fourier transform.

Imagine an ideal point source hemispherical radiator mounted on the exact center of the end of a long cylindrical solid. Such a radiator will exhibit a hemispherical radiation pattern that is independent of frequency. In addition, let us suppose it exhibits minimum phase characteristics and has flat frequency response over all frequencies. If we now excite the radiator with a discrete-time impulse of duration 0.025 mS, it will move in response to the impulse and stimulate a hemispherical acoustic impulse moving away from the point source at the speed of sound. Since the radiator is perfect, the acoustic impulse will have a shape identical to the discrete-time impulse.

Everything is very easy to visualize until the edge of the impulse reaches the edge of the cylinder. When the impulse reaches the edge of the cylinder, there is a sudden loss of support as the impulse is now free to radiate behind the face of the cylinder, not just in front of it. In this way, the impulse ‘diffracts’ or ‘scatters’ behind the face of the cylinder. Interestingly, this scattering is frequency independent, but angle dependent. So if we measured the acoustic signal behind the cylinder, we would find that it is an impulse identical to the one formed by the radiator but somewhat diminished in magnitude. Now, few of us set up our favorite listening spot behind our loudspeakers, so it makes sense to try to understand what happens in front of the loudspeaker. Due to the loss of support at the edge of the cylinder, the impulse will partially collapse as some of the pressure ‘leaks’ backwards and this causes a secondary impulse to scatter in the forward direction. Like the impulse scattered behind the cylinder, the forward-scattered impulse will also be frequency independent but angle dependent. Unlike the backward-scattered impulse, though, the forward-scattered impulse will have the opposite polarity as the original impulse. Now imagine a microphone located in front of and on the cylinder axis, far away from the cylinder. What will the microphone measure? First, the impulse from the radiator will be picked up then, delayed by an amount equal to the radius of the cylinder divided by the speed of sound, the forward-scattered impulse will be measured.

Now, as stated previously, neither the forward nor the backward-scattered impulses display frequency dependence. However, taken together, the direct and forward-scattered impulses will result in frequency dependence through constructive and destructive interference. Figure 1 and Figure 2 show the time and frequency domain behavior of the impulse as measured by a microphone located in front of and on the cylinder axis, far away from the cylinder. The radius of the cylinder is 1 meter and the radiator is mounted in the center of the baffle.