Latent Heat of Vaporization

Introduction :

Latent is a Latin word which means hidden. Latent heat is hidden heat, which a body absorbs or releases when it changes form one state to another.

Latent heat of vaporization of a substance is the amount of heat required to change one unit mass of that substance from liquid to gaseous state. During this process, the temperature of the substance remains constant. The heat absorbed in the process used to change the state of that substance from liquid to gaseous state. The heat energy increases the internal energy of the substance in form of change of state with no rise in temperature. A substance starts changing its state from liquid to gaseous state upon reaching its boiling point. When change of state starts taking place, the temperature of the liquid becomes constant at the boiling point. The heat absorbed there after used up in changing its state from liquid to gaseous state.

Latent Heat of Vaporization :

Similar to the latent heat of vaporization, there is latent heat of fusion. Just like the latent heat of vaporization, it is the heat required by a substance to change from solid to liquid state. In this case, also there is no rise in temperature when change of state takes place.

Latent Heat of Vaporization :

For a particular substance, Latent heat of vaporization per unit mass is more than its specific heat. For example, Latent heat of vaporization of water is 2260 J/g whereas its specific heat is just 4.2 J/g per degree centigrade rise in temperature. That is why burn caused by steam at 100 degree centigrade is more severe than burn caused by water at 100 degree centigrade.  Similarly, ice at zero degrees centigrade is cooler than water at zero degrees centigrade.

We can conclude one should be more cautions in burns caused be steam because latent heat of vaporization comes into play causing more severe burns.

J.J. Thomson's atomic model

Joseph John Thomson was Danish Physicist, who discovered the 'electrons' in 1897 and put forward his famous ‘plum pudding model’ of atom in 1904.The structure of atom was put forth by many scientists. John Dalton, J.J. Thomson, Rutherford and Bohr are the important scientists who worked in this field.

The following are the work of various scientists in framing the structure of atom:

• John Dalton discovered that matter is made of very small particles called atoms which can not be divided.
• J.J. Thomson discovered electrons and found that the atom can be divided and it is made of positive core and negatively charged particles embedded in it.
• James Chadwick discovered the protons.
• Goldstein discovered neutrons.
• Rutherford discovered that atom has a positive central core called nucleus and the electrons move around the nucleus in great speed.
• Bohr stated that the electrons move around the nucleus in a definite energy levels called shells and gave the explanation for the stability of atom.

Discovery of Atom

It was John Dalton, who stated that the matter is made of indivisible small particles called atoms. Atom means 'that which can not be divided'. This model was discarded by J.J. Thomson when he discovered the electrons.

J.j. Thosmson Atomic Model

 Michael Faraday worked on the passage of electricity through liquids while Thomson worked on the passage of electricity through gases. During this experiment, Thomson discovered the electrons.
According to Thomson, when a glass tube fitted with two electrodes filled with a gas at low pressure and when a high voltage of electricity is applied, some rays are generated from the cathode. He named these rays as cathode rays. When two charged plates are placed on either side of this discharge tube, these rays (cathode rays) are attracted to the positive plate. Hence he said that the cathode rays are made of negatively charged particles. He called these particles as ‘corpuscles’. Corpuscles mean particles. G. J. Stoney named them as ‘electrons’

In J.J. Thomson atomic model, the atom consists of a sphere of uniform distribution of positive charge with electrons embedded in it. The number of positive particles is equal to the number of electrons and the 'atom as a whole is eclectically neutral'. This model accounted for the neutrality of atom. This model is popularly known as"plum pudding model", like negatively-charged "plums" surrounded by positively-charged "pudding".

But later Rutherford proved that the electrons are not embedded in the positive sphere, but they revolve around the positive central core and he named it as nucleus

Molecular Formula for Alkynes

Introduction :

Alkynes are hydrocarbons which contains carbon-carbon triple bond. They show neither geometric nor optical isomerism. The simplest alkyne consist of one triple bond i.e. ethyne (HCCH) which is commonly termed as acetylene. The structural formula of acetylene is



Molecular Formula and Structural Formulas:

The alkynes consist of compounds which are based on carbon and hydrogen series containing leastways one triple bond. The alkyne is a homologous series having the formula of CnH2n-2, where n is any integer which is greater than one.

In the chain of long alkynes, the carbon atoms added are closed to each other via single covalent bonds. Each carbon atom in the alkynes is associated with sufficient hydrogen atom to complete the valency of carbon as four. In alkynes, if there are four or more than four carbon atoms, the triple bond can be situated in different positions next to the chain which results in the formation of isomers.

For example, the alkyne of molecular formulas C4H6 has two isomers,



As alkynes have restricted rotation because of the presence of triple bond, they do not hold stereo isomers as alkenes because there is sp hybridized bonding present in a carbon-carbon triple bond. The maximum separation is 180o between the hybridized orbitals in the sp hybridization so the molecule is in linear form. Thus the alkynes are located in straight line because of this stereo isomers are impossible.

Physical Properties of Molecular Formula for Alkynes:

Most of the alkynes are less dense than water but some are exceptions.

Chemical Properties of Molecular Formula for Alkynes;

Alkynes are more polar than alkanes and alkenes. Liquid alkynes are non-polar solvents so immiscible in water. Alkynes having low ratio of hydrogen atoms to carbon atoms are highly combustible.

These alkynes are highly reactive so can be easily broken into alkanes and alkenes. They store large amount of chemical energy that’s why highly exothermic when broken. The released heat can cause rapid expansion so care must be taken when managing with alkynes.

Conclusion on Molecular Formula for Alkynes:

The triple carbon bonds are formed in alkenes due to absence of hydrogen’s. Thus they allow carbon bonds to be stronger, because of the nucleus central force which pulls in nearby atoms.

Benzene Molecular Formula

Introduction:

Carbon has valency of 4.Hydrogen has valency of 1.Untill the discovery of benzene,no compound with empirical formula C_nH_n was discovered.As such benzene with same empirical formula posed a great challenge.It was predicted that the molecule would invariably contain unsaturation.

Progressive Attempts on Benzene Molecular Formula:

Since it was first isolated and identified in 1825,the knowledge of structure of eluded the chemists for many decades

The existence of double bond in ethene was discovered by Scottish chemist Alexander Brown in 1864.However the discovery of the probable structure of C6H6 continued to dodge the chemists.It was so because never before was any structure derived for a compound with the empirical  formula C_nH_n.

The chemists were confused as to how all the valencies of carbon would stand satisfied in such a compound.

Kekule's Contribution in Benzene Molecular Formulas

Simultaneously attempts were also made by Adolph Carl Ludwig Clause ,Henry Armstrong etc. to propose certain structures.However they failed.

It was only in 1865 that Kekule could make a breakthrough in devising this structure.He devised the structure with hexagonal ring. He said that he had discovered the ring shape of the benzene molecule after having  day-dream of a snake seizing its own tail .

This structure  met with lot of criticism in the beginning and was further refined.In 1872 he put forth that the atoms are oscillating and were in reverse and forward collision with the neighbouring carbon atoms.

pi bonds in benzene

Kekule put forth the correct structure in 1865.According to it ,benzene has aromatic structure. He revealed that he had discovered the ring shape of the benzene molecule after having  day-dream of a snake seizing its own tail .This structure  met with lot of criticism in the beginning and was further refined.
The only way in which this could be explained is pi bonds in the aromatic ring.

Unconventional pi bonds

It means it consists of a conjugated planar ring system with delocalized pi electron clouds.These electtrons which form the double pi bond keep on 'hopping' between subsequent bonds.This also can be expressed in following sentence.

The electrons for C–C bonding are distributed equally between each of the six carbon atoms.
Average length between the C-C and C=C is at 0.139 nm. This is called as 'resonance'. Resonance adds to the energy of the structure. As a result benzene is more stable by 150 kJ mol^-1than predicted by Kekule because of resonance.

Each carbon atom is attached to one hydrogen atom in addition to two carbon atoms.The electrons of the pi bonds keep on oscillating forth and back.In this way an the valencies of the atoms stand satisfied,albeit in a unconventional way.Thus in order to facilitate this,the structure would be planar and not three dimensional.This enhanced stability is the fundamental property of aromatic molecules that differentiates them from non-aromatic molecules.

Because of these pi bonds, benzene undergoes nucleophilic as well as electrophilic addition reactions at one end of any double bond.

Structure with Respect to Moleculr Formula

The structure of benzene has aromatic nature.
It means it consists of a conjugated planar ring system with delocalized pi electron clouds.The electrons for C–C bonding are distributed equally between each of the six carbon atoms. Each carbon atom is attached to one hydrogen atom.The electrons of the pi bonds keep on oscillating forth and back.In this way an the valencies of the atoms stand satisfied,albeit in a unconventional way.Thus in order to facilitate this,the structure would be planar and not three dimensional.This enhanced stability is the fundamental property of aromatic molecules that differentiates them from non-aromatic molecules .

The discovery of ring structure of benzene has led to vast field of aromatic compounds in organic chemistry. Many important chemicals are derived from benzene by replacing one or more of its hydrogen atoms with another functional groups.e.g toluene,phenol etc.The ring structure is also the basic unit of many biochemicals like hormones.

Brownian motion

The zig-zag, random, irregular motion exhibit by small particles of matter suspended in a fluid is called as Brownian motion or Brownian movement. This type of movement can observed in almost all type of colloidal suspensions such as liquid in liquid, gas-in-liquid, solid in liquid, liquid-in-gas and solid-in-gas.

Let’s define Brownian motion. Brownian motion definition can write as the random motion of particles in all possible directions.

Brownian motion was first observed by botanist Robert Brown in 1827 in pollen grains floating in water. The movement of particles is not depends on any external force. The velocity of particles is proportional to the square root of the temperature. Generally particles of about 0.001 mm in diameter can show Brownian movement as these particles are small enough to share in the thermal motion, yet large enough to be seen with an ultra-microscope.

In 1905 Albert Einstein explained, ‘What is Brownian Motion’ and purposed the theoretical treatment of Brownian motion. Further Jean Perrin made a quantitative experimental study and proved the dependence of Brownian motion on temperature and particle size and also provided verification for Einstein's mathematical formulation.

Brownian movement can easily observe in colloidal solution. The colloidal particles and molecules of dispersion medium are in continuous collisions due to their constant motion. Due to their motion, particles pass their kinetic energy and strike in all sides results into zigzag movement. That is the reason when colloidal solutions are viewed under an ultra microscope; particles are seen continuously moving in a zigzag path. The main cause of Brownian movement is the unequal bombardments of the moving molecules with other particles. Like in colloidal solution, the molecules of dispersion medium continuously attack on colloidal particles from all sides and impart momentum to them.

Due to collisions between molecules, colloidal particles change its direction and again move in another direction to colloid with another molecule. The collision between molecules remains continuous and results in a random zigzag movement of particle. As the size of colloidal particles increases, the Brownian movement decreases and that is the reason suspensions cannot exhibit this type of movement.

The stability of colloidal sol is mainly depends upon the Brownian movements of particles. As Brownian movement opposes the gravitational forces acting on colloidal particles, therefore particles would not settle down. These movements are also helpful to explain the force of gravity on colloidal particles.

So we can briefly describe Brownian moment of a particle as the zig zag motion of the particles in simple words. Brownian moment hence plays a significant role when we describe the characteristics of the particles. 

Stefan Boltzmann Law Radiation

Introduction :

The emission of electromagnetic waves at the expense of the internal energy of the bodies is known as thermal radiation. Theoretical explanation of the nature of black body radiation finally led to the concept of energy quanta which is the first step toward quantum mechanics enabling us to investigate the secrets of atomic structure and other properties of the substances.

Mathematical Equation for Stefan Boltzmann Law Radiation

oseph Stefan analysed the experimental data about the radiation of the bodies at various temperature and concluded that Emissive power of a (black) body is proportional to the forth power of the absolute temperature
Mathematically P  =  `sigma` AT² .,     where A is the surface area, T is temperature of eh surface in Kelvin scale and `sigma`  is the universal constant called Stefan's constant and its value is 5.670 x0 10^-8 W / m² K⁴ . 
Stefan's law involved the temperature in Kelvin scale not in Centigrade scale. The fourth power of temperature indicates how sensitive the power emitted by a body to temperature changes. Initially  Stefan concluded that the  above equation is valid for any body as he did not perform experiments with black bodies. Later Boltzmann on the basis of principles of thermodynamics showed that the equation is valid only for black bodies. Hence the statement leading to the above equation is called Stefan-Boltzmann law.

Definition for Stefan-boltzmann Law Radiation

A body emits radiation that will be proportional to fourth power of absolute temperature and for any body Stefan-Boltzmann law can be given by        
P  =  e_`lambda` `sigma` AT⁴ .........................(1)
where e_`lambda` is emissivity of the body. Its value ranges from 0 to 1.
For a black body   e_`lambda`  =  1 and for a perfect reflector  e_`lambda` =  0.  For example, for polished aluminium   e_`lambda` = 0.05 as it is an excellent reflector , for soot (carbon black) e_`lambda` = 0.95. Human skin has emissivity about 0.97 in infrared region of electromagnetic waves.
If a body with surface area A and temperature T is kept in surroundings with temperature T_s , it simultaneously emits and absorbs thermal radiation till dynamic thermal equilibrium is attained. Then the net rate of heat flow is given by
P_net      =           P_emitted   -   P_absorbed.
From equation (2) ,  P_emitted  =    e_`lambda` `sigma` AT⁴    and P_absorbed =   e_`lambda` `sigma` AT⁴_s .
Hence  P_net         =        e_`lambda` `sigma` AT⁴      -           e_`lambda` `sigma` AT⁴_s                =        e_`lambda` `sigma` A(T⁴ - T⁴_s ).
After the thermal equilibrium is attained, the body and the surroundings are at the same temperature, the body emits the energy at the same rate as that it absorbs. Hence  P_net  =  0.
If  T  >  T_s the body emits more thermal radiation than it absorbs.
If T < T_s the body absorbs more thermal radiation than it emits.

Lithium

Introduction:

Lithium is the first of group I alkali element. Lithium was discovered by Arvfedson. Litium is rare metal, but is widespread. It is prepared by electrolysis of fused lithium chloride. Amblygonite, Lepidolite, Spodemenn is the ores of lithium. Lithium is a soft, lightest metal. Lithium is used in batteries and medicinal fields.

Lithium

• Symbol -Li.
• The atomic number of lithium is 3.
• The atomic mass of lithium is 6.94.
• The electronic configuration of lithium is 1s² 2s¹.
• Lithium is a solid metal which is silvery in its purest form.
• The valence number of electron is 1. Its tend to loss one electron readily to form li⁺ ion.

Properties of lithium:

Physical properties of Lithium:

The following are physical properties of Lithium:

• Lithium is a soft silvery metal. Fresh lithium is silvery but when it is exposed to air it becomes grayish due to oxidation.
• Lithium is lightest of all the metals, the density is very less. The density of lithium is about 0.534 grams per cubic centimeter.
• Lithium hardness is 0.6 on Mohs scale. Mohs scale is used to represent hardness of the material. We can scratch the lithium with our fingernails.
• The structure of lithium is body centric.
• Lithium is a highly reactive metal, readily forms oxides on the metal surface.
• Lithium is a lightest metal and is a good conductor of heat and electricity.
  • Electrical conductivity – 0.108 10⁶ / cm
  • Thermal conductivity- 0.847 W / cmK
• Lithium posses high boiling and melting points.
  • Boiling point of Lithium is 1,335 degree Celsius
  • Melting point of Lithium is 180.54 degree Celsius.
• Lithium has highest specific heat capacity about 3.6 j/gk

Chemical Properties of Lithium:

The following are chemical properties of Lithium:

• Lithium is highly reactive so it is kept under liquid paraffin or oil to prevent oxidation.
• Lithium reacts with oxygen at high temperature to form oxides, at normal temperature it reacts slowly.
• Lithium is the alkali metal that reacts with nitrogen that forms a black nitrure.
• Lithium reacts with halogens produces salts of lithium.
• Lithium reacts readily with water, liberates hydrogen and forms lithium peroxides.
• Lithium produces crimson red color flame during burning.

Velocity of a Reactions

Introduction to Reactions:

The reactions are defined as " the total number reacting special whose concentration actually alters during the course of chemical reactions. In other words, it is the number of concentration terms which determines the dependence of rate of reactions. For a general reactions numerical value of order of reactions are the sum of all the exponents to which the concentrations in the rate equation are raised.

Velocity of a Reactions:

• The velocity or rate of chemical reactions can be defined and measured as "the rate of formation of  one or more of its products or as the rate of consumption of one or more of its reactants".
• If the reactions are homogeneous and occurs entirely in the gaseous phase, the partial pressure of its components could be measured, and if the reactions takes place in solution.
• Thus, the units of velocity of a reactions in solution will be units of concentration per unit time.
• The velocity of a reactions, depends on the concentration or pressure of the reactants.
• As the concentration of the reactants keep on decreasing from moment to moment so, velocity of a reactions decreases with time.
• In order to decide  the velocity of  reactions at any time.

Expressing velocity of reaction:

• The velocity of reactions are measured in terms of either the rate of decrease in concentration of reaction(s) or the rate of increase in concentration of product(s). Thus, for the reactions A`->` B.

• The velocity of reaction is given by:

`(-d[A])/(dt)` =`(+d[B])/(dt)`

• It must be clearly understood that the velocity of reaction is invariably a positive quantity.
• The minus sign given to -d[A]/dt simply indicates that the concentration of the reactant, A is falling.
• While positive sign given to +d[B]/dt implies that the concentration of the product, B is increasing with the time.

Simultaneous Reactions:

• Some of the simultaneous reactions are:

Parallel reactions:

• The reactions giving the main product is called main reactions, while the other is called parallel or side reactions.
• By altering the conditions of the experiment, the relative rates of the side reactions can be varied and sometimes to such an extent that a side reaction is changed into main or principal reactions and vice-versa.

Consecutive reactions:

• This reactions in which the first reaction product is subsequently converted into a second product.

Consider the process,

Reversible reactions:

• In which the rate of the back reaction in significant.

• Reaction products react among themselves to form the original reactants at significant speed.

Electromagnetic waves transverse or longitudinal

Introduction:

Before going to learn whether the electromagnetic wave is transverse or longitudinal .Let us have a brief review on wave and its characteristics

Wave motion:
 It is a process of transferring energy in a medium in the form of disturbance due to repeated periodic motion of the particle in the mean about their mean position in which the energy is handed over from one particle to other particle by leaving their mean positions.

Mechanical Wave:
A mechanical wave is a periodic disturbance which can be produced only in a material medium and its transfer of energy from one point to other without there being a direct contact between  the two points.

Two types of mechanical waves:

Mechanical waves are classified into

1) Transverse waves

2) Longitudinal waves 

Electromagentic Waves are Transverse

Electromagnetic waves characteristics are similar to transverse waves.
If the particles at a medium vibrate at right angles to the direction of the propagation of the energy then that wave is called as transverse wave. Such waves are produced on the surface of water, in musical instruments. If the stretched strings, the energy the energy travels outwards and the particle of the medium vibrates up and down.

Electromagnetic waves are transverse waves.
The following terms are used in the study of transverse wave or electromagnetic wave:

Amplitude:
It is the maximum displacement of particles from the mean position. The displacement may be in either direction of the mean position.

Period: The period of a wave is the time taken by a wave to complete one oscillation

Frequency: Number of vibrations made by a particle of the medium in one second

Crest and trough of a transverse wave: A crest is a point of a transverse wave which at any instant have the maximum positive  or upward displacement.

Trough: This is defined as the maximum negative or downward displacement.

Wavelength:
For a electromagnetic wave the distance between consecutive crest and trough is called as wave length.
Wave velocity is the energy at which wave is propogated.

Electromagentic Waves are Longitudinal Waves

Longitudinal waves:
Electromagnetic waves can travel through vacuum. Example of the electromagnetic waves is the light waves. This is because light waves are not mechanical waves. A light wave is a periodical disturbance which can travel through vacuum.

These waves are discovered Maxwell and consists of vibrating electric  and magnetic fields since such fields can produce in vacuum and can be propagated in vacuum. the light waves, gamma waves, radio waves and X-rays are some of the examples of electromagnetic waves.

Electromagnetic Wave Intensity

Introduction :

The electromagnetic wave intensity is nothing but the measure of the intensity of the electromagnetic wave in free space or in any medium. It generally depends on the velocity of the electromagnetic wave. It is proportional to the square of the amplitude of the electric or magnetic field.

Before giving a proper definition of electromagnetic wave intensity we first try to understand what electromagnetic waves are. The electromagnetic waves are nothing but the waves produced due to an accelerating or oscillating charge. This wave contains both electric and magnetic field vectors which are perpendicular to each other as well as perpendicular to the direction of the wave propagation.

Define Electromagnetic Wave Intensity:

The electromagnetic wave intensity is defined as the energy crossing per second per unit area perpendicular to the direction of propagation of electromagnetic wave or the average power per unit area transported by an electromagnetic wave.

Example of Electromagnetic Wave Intensity:

For proper understanding of the electromagnetic wave intensity, we consider an example in which the electromagnetic waves are propagated along X-axis with the speed of light. Consider an imaginary cylinder along the X-axis with area of cross section A and length c Δt and the electromagnetic waves are incident normally to the area A and crosses the cylinder as shown in Fig.1. Let u_av be the average energy density of the electromagnetic wave.

         Fig.1 Imaginary cylinder
The energy of electromagnetic wave (U) crossing the area of cross section at P normally in time Δt is the energy of wave contained in a cylinder of length c Δt and area of cross section A. It is given by
                                                            U =u_av (c Δt) A
The intensity of electromagnetic wave at P is
                                                            I = U / A Δt
                                                              = u_av c Δt A / A Δt
                                                              = u_av c
In terms of maximum electric field
                                                            u_av = ε₀ E₀² / 2
so,                                                        I = ε₀ E₀² c / 2 = ε₀ E²_rms c
In terms of maximum magnetic field
                                                            u_av = B₀² / 2μ₀
so,                                                        I = B₀² c / 2μ₀ = B²_rms c / μ₀

Common Family Problems

Introduction :

Like there is no bread without holes, there does not exist a family without family problems.  All members in the family cannot be alike. Thus the differences in nature give rise to difference in opinion which leads to conflicts or misunderstandings.

Common Family Problems:

some of the common family problems are misunderstandings between the members of the family, non-cooperation by children, jealousy and enmity between sibling, financial problems, relationship problems between spouses, problems in handling the daily chores, problems with other relatives of the family and problems due to child birth and or problems due to a death in the family.

While there is no one solution for all problems, there is no solution for all problems either.Each problem has to be taken on an individual basis and the family members need to discuss problem resolution.
Some of the problems like lack of sensitivity or understanding by a child can be caused due to indiscipline. The root cause could also be that the child needs special care. Unfair treatment of one or both parents towards children can cause enmity and jealousy between siblings. Parents need to avoid pleasing one child at the expense of the other.

Divorce or separation of the parents can be a very big emotional burden for the children to carry. The whole process needs to be handled carefully with regular psychological consultation for the children.

Disrespect towards family member or outsiders, crossing boundaries, lack of empathy and violent behaviour by a family member needs to be curbed as soon as it is noticed and the family members need to take due care to identify what is causing such behaviour and tackle it.Age differences can cause differences in understanding and responding to different scenarios, family members need to recognize this and talk it out.

Conclusion to Common Family Problems:

While there is scope for a lot of problems in a family, the very reason that it’s a ‘family’ means that the members can handle these common problems amicably and live peacefully. Every member in the family should contribute towards ensuring harmony and love between the family members. This way most of the common family problems can be avoided.

Pulse Amplitude Modulation

Introduction:

In analog modulation systems, some parameter of sinusoidal carrier is varied in accordance with the instantaneous value of the modulating signal. In pulse modulation systems, the carrier is no longer a continuous signal but consists of a pulse train, some parameter of which is varied in accordance with the instantaneous value of the modulating signal.

Types of Pulse Modulation Systems:

There are two types of pulse modulation systems:
(1) Pulse Amplitude modulation.(PAM)
(2) Pulse Time modulation. (PTM)

Pulse Amplitude Modulation

In PAM, the amplitude of the pulses of the carrier pulse train is varied in accordance with the modulating signal; whereas in PTM, the timing of the pulses of the carrier pulse train is varied.
Figure shown below explains the principle of PAM. A baseband signal f(t) is shown in (a) part, and carrier pulse train f_c(t) is shown in the (b) part. The frequency of the carrier pulse train is decided by the sampling theorem. According to the sampling theorem, if a modulating signal is band limited to X Hertz (i.e., there are no frequency components beyond X Hz in the frequency spectrum of the modulating signal), the sampling frequency must be atleast 2X Hertz and, hence, the frequency of the carrier pulse train must also be atleast 2X Hz. A pulse amplitude modulated signal f_m(t) is shown in the figure in (c) part. It can be seen that amplitude of the pulses depends on the value of f(t) during the time of the pulse. The PAM signal f_m(t) is known as discrete time signal, as this signal is discrete on time axis and continuous on amplitude axis.

In the above figure, the baseband signal f(t) is shown to have only a positive polarity. In practice, however, we can have a baseband signal with a positive as well as negative polarity. But, in such a case, the modulated pulses will also be of positive as well as negative polarities. As the transmission of such a bipolar pulses is inconvenient; a clamping circuit is used so that we always have a base band signal with only the positive polarity. 

Vsepr theory chart

Introduction :

The two scientists R.S Nyholmm and R.J Gillespie proposed the VSPER theory in 1957. VSEPR theory helps us in explaining the repulsion caused between the atoms, bonds and lone electron pairs in a molecule. VSEPR theory was developed to predict the shapes of the molecule in which atoms are bonded, including the repulsion facts.

VSEPR Theory Definition:

Valence Shell Electron Pair Repulsion (VSEPR) theory is a phenomenon used in chemistry to predict the shapes of the individual molecules based on the repulsion acting between the electrons pairs in a molecule. The other name if VSPER theory is Gillespie-Nyholm theory, named after its two main developers. In this theory, it is explained that, valance electron pairs surrounding an atom mutually repel each other and hence they will arrange themselves in such a geometry, which minimizes their repulsion between electron pairs. The number of electron pairs around an atom, that is bonding and non-bonding are called steric number. The number of electron pairs in the valance shell of a central atom is concluded by drawing the Lewis structure of the molecule in which all lone electron pairs will be shown with bonds.
Diagram of VSEPR theory Chart

                                   

Postulates of VSEPR Theory:

The main postulates of VSEPR theory are:

• The total number of electron pairs (bonding and non-bonding) determines the shape of the molecule and on the orientation of the electron pairs around the central atom.
• To minimize the repulsion between the atoms, the electron pairs arrange themselves fare away from the central atom.
• The electron pairs around the central atom can be shared electron pairs or lone pairs. The shared electron pairs are known as Bond pairs.
• The strength of repulsions between different electron pairs is in the order:

Lone pair - Lone pair > Lone pair - Shared pair > Shared pair - Shared pair.

Prediction of shapes using VSEPR theory

 VSEPR theory could predict the shapes of a molecules correctly . The following examples prove this :
a) BeCl₂ has two single Be-Cl bonds and these two bond pairs of electrons on Be atom are oriented farthest in the opposite directions to have minimum repulsions between them . BeCl₂ is a linear molecule . Similarly CO₂ molecule has two carbon - oxygen double bonds . These bond pairs of electrons are oriented in opposite directions to have minimum repulsion . Hence , CO₂ is called linear molecule O = C = O .
b) In BCl₃ there are three B-Cl single bonds or there  are three bonded electron pairs around 'B' in the valence shell and they are oriented farthest apart to have minimum repulsion among them . Hence BCl₃  molecule has trigonal planar structure with `|__ClBCl` bond angle 120^o .
c) All the four electron pairs in methane (CH₄) are bond pairs only. Therefore , the molecule is tetrahedral with a bond angle of 109^o29' .
d) Nitrogen in NH₃ has four electron pairs .
e) In water molecule, the central atom , oxygen has two lone pairs and two bond pairs of electrons . The number of lone pairs on oxygen is grater than those on nitrogen in ammonia . Due to stronger lone pair - lone lone pair repulsions , the bond angle decreases to 104^o30'. Thus , the water molecule is 'V' shaped and not linear.

Conclusion on Vsepr Theory:

VSEPR theory proved very useful in predicting the shapes of all molecule sand it also helps in explaining the distortion of angles between the atoms. VSEPR theory also explains the idea why the shape of some molecule is different with the others.