Introduction to electronics : Part 3

Wave Mechanics:

Schrodinger carried the implication of  the wave nature of the electron further and developed a branch of physics called wave mechanics or quantum mechanics.He argued that if De Broglie's concept is correct,it should be able to deduce the properties of an electron system from the properties of an electron system from a mathematical relationship such as wave equation of electromagnetic theory,optics,mechanical vibrations,etc.,

Such a wave equation equation is given by,

-------------------> eqn (1)
where,



and  is the velocity of the wave and the time.
The physical meaning of   depends upon the problem under consideration. It may be one of the component of electric field,the mechanical displacement,the pressure etc., depending upon the physical problem.
We can eliminate the time variable by assuming a solution in the form,

--------------------> eqn(2)
Then equation (1) becomes,

-------------------> eqn (3)
where,


From De Broglie relationship,

we can write,
 -------------> eqn (4)
where kinetic energy  is the difference between the total energy W and the potential energy U.
Here W = kinetic energy + potential energy which is represented as





Substitute eqn (4) in eqn (3),we get the time-dependent
 -------------> eqn (5)

The  in eqn(5) is called the wave function,it must describe the behaviour of the particle.It is found that the proper interpretation of  is that it is a quantity whose square the probability gives the probability of finding an electron.
In otherwords,   is proportional to the probability that the electron is in the volume dxdydz  and the point P(x,y,z) in space.The wave function  in above equation describes the behavior of the particle.It is found that the proper interpretation of wave function ,is a quantity whose square gives the probability of finding the electrons.Therefore the wave function must be normalized such that it becomes unity,thus indicating that the probability of finding electron must be unity.

Limitations of Schrodinger wave equation:

1.Schrodinger equation could be used to find only about the probability that the electron can be found in the neighborhood  of  a precise point P but could not attempt to locate the particle.

2.The solution of Schrodinger's equation,subject to the proper boundary conditions yields the allowed energies of the particles and its wave function.Therefore it becomes complex to solve higher order functions of wave functions.

Electronic Structure of Elements:

The solution of Schrodinger equation for hydrogen or any multi electron atom need not have radial symmetry.The wave function may be a function of azimuth and polar angles as well as of the radial distance.It turns out that,in general case,four quantum numbers are required to define the wave function.the total energy,orbital momentum,the component of the angular momentum alon a fixed axis in space and the electron spin are quantized.

The four quantum numbers are as follows:

1. The Principal quantum number:

It is an integer 1,2,3,... and determines the total energy associated with a particular state. The number may be considered to define the size of the elliptical orbit,and it corresponds to principal quantum number n of Bohr atom.

2.The orbital angular momentum quantum number :

It takes the values from 0,1,2,3,....,(n-1).This number indicates the shape of classical orbit.

3.The orbital magnetic number:

It may have the values -l,.....,-4,-3,-2,-1,0,1,2,3,4,....l.This number gives the orientation of classical orbit with respect to an applied magnetic field.The magnitude of the component of angular momentum along the direction of the magnetic field is given by m(h/(2)(3.14)).

4.Electron spin:

In order to explain certain spectroscopic and magnetic phenomena, Uhlenbeck and Goudsmith,in 1925,found it necessary to traversing its orbit around the nucleus,the electron must also rotate about its own axis.This intrinsic electronic angular momentum is called electronic spin. when an electron system is subjected to a magnetic field,the spin axis will orient itself either parallel or anti-parallel to the direction of field.The spin is thus quantized to one of the two possible values i.e.,+1/2,-1/2.

Pauli's exclusion principle:

Periodic table of chemical elements may be explained by invoking a law by invoking a law enunciated by Pauli in 1925.He stated that no two electrons in an electronic system can have the same set of four quantum numbers.This statement that no electrons may occupy the same quantum state is known as the Paul exclusion principal.

The inner shell electrons of the atoms are very strongly bound to an atom,and cannot be easily removed.That is,the electron closest to the nucleus are the most tightly bound and have the lowest energy.The atoms for which the electrons exist in closed shells form a very stable configuration.For example,the inert gases He,Ne,A,Kr and Xe,all have either completely filled shells or at least completely filled sub shells.If we consider the elements like carbon,silicon and germanium,each of these elements has completely filled sub shells except for the outermost p shell,which contains only two of the six possible electrons.
The reason for considering 4A group elements is that these metals in crystalline form can behave as a conductor,semi conductor and insulator.

This ends the introduction of electronic devices and circuits.

Disclaimer:

I have created this blog for educational purpose,so for that i have written the content by referring many books,web pages.I have also uploaded google images and you tube videos for the better understanding of concept and I would also like to inform you that I am not responsible for the ads which are being posted in my blog.

Introduction to electronics :Part2

Ionization:

The loosely bounded electrons in an atom generally have more energies, so these electrons move to stationary states which are farther and farther away from the nucleus.when the electron have high energy in such a level that it can completely move out of the field due to influence of ion and gets detached from it. Then the atom is said to be ionized.The alkali metals have lowest ionization potentials,where as,inert gases have the highest values.

Collision of electrons with atom:

In order to excite or ionize an atom,energy must be supplied to it.This energy may be supplied to the atom in various ways.

One of the most important way is through electron impact. other methods of ionization or excitation of atoms are considered below.

• Suppose that an electron is accelerated by potential applied to the discharge tube.When electron collides with an atom,one of the several effects may occur:
• A slowly moving electron suffers an elastic collision i.e., one entails an energy loss only as required by the laws of conservation of energy and momentum.
• The direction of travel of electron will be altered by collision although its energy remains substantially unchanged.Since this follows the fact that the mass of gas molecule is large compared with that of electrons.
• If the electron possess sufficient energy,the amount depending upon particular gas present,it may be transfer,enough of its energy to the atom to elevate it to one of the higher quantum states.The amount of energy necessary for this process is called excitation or radiation or potential of an atom.
• If the impinging electron possesses a higher energy,say,an amount at least equal to the ionization potential of the gas,it may deliver this energy to an  electron of the atom and completely remove if from the parent atom.

Note:

It must not be presumed that incident electron must possesses an energy corresponding exactly to the energy of stationary state in an atom in order to raise the atom into its level. If the bombarding electron has gained more particular state,the amount of energy in excess of that required for excitation,then this excess energy will be retained by incident electron as kinetic energy after the collision or if the process of ionization has taken place,the excess energy divides between the two electrons.

Collision of photons with atoms:
When a photon collide with an atom (say of gas) in excited state, the atom may absorb a photon of frequency V and it may have a transition from lower energy states  E1 to higher energy state E2,where,   

                                                                                        

It should be noted that the atom will not be excited unless the energy of photon corresponds  exactly to the energy difference between the two stationary states of the atom.when  a photon is absorbed by an atom,the atom is elevated into excited state,the excited  atom now returns to its ground state in one jump or in several steps,when a photon is not absorbed by an atom, the atom now returns to the ground state after falling into one or more excitation levels.
The atom exists in several photons corresponding to the energy difference between successive excited levels into which the atom falls.the newly emitted photons have energy less than the energy of impinging photon .so the frequency of emitted photons are different from that of incident photon. If the frequency of impinging photon is high,it may cause ionization of the atom.in this case, the photon vanishes with the appearance of an electron and a positive ion. Here it is not essential that the impinging photon must posses energy exactly equal to the ionization energy of the atom but it must posses energy exactly equal to the ionization energy of the atom but it must posses at least this much energy. When the photon possesses energy exceeding the ionization energy,the excess of energy appears as kinetic energy of emitted electron and positive ion.

Meta stable states:

Stationary states may exist by excitation of electron bombardment but not by photo excitation,then the levels that are so formed are called meta stable states.A transition from a meta stable level to normal state with the emission of radiation has a very low probability of taking place.

The long lifetime of the meta stable states arises from the fact that the transition to the normal state with emission of a photon is forbidden.The energy of meta stable state can be expanded so that the atom may return to its normal in two cases:

1. When the collision of meta stable atom takes place with another molecule,it gives its energy to other molecule,in the form of kinetic energy of translation or potential energy of excitation.
2. When an electron in meta stable state receives additional energy,then the meta stable atom may thereby be elevated to a higher energy state from which a transition to normal level can take place,or else it may be ionized. 

Note:
If the meta stable atom diffuses to the walls of the discharge tube or to any of the electrodes, therein , either it may liberate its energy in the form of heat or the meta stable atoms might induce secondary   
emission.

The wave properties of matter:

When an atom absorb a photon of frequency f and move from the energy level E1 to higher energy level E2 then,

                                                 

since a photon is absorbed by only one atom,the photon acts as if it were concentrated in one point in space.

According to De-Broglie hypothesis, the dual character of atom i.e., wave and particle nature is not only limited to radiation but also characterized by particles such as electrons, atoms, molecules or macroscopic masses. He has calculated the mass m of the particle traveling with a velocity v when a wavelength is associated with it. Thus it is given by,

where p is the momentum of the particle.

The existence of such matter waves was demonstrated experimentally by Davinson and Germer in 1927 and 1928 respectively.

              

We can make use of wave properties of a moving electron to establish Bohr's postulates that a stationary state is determined by the condition that the angular momentum must be an integral multiple of  h/2

It seems reasonable to assume that an orbit of radius r will correspond to a stationary pattern.In other words, a stable orbit is an orbit whose circumference is equal to the electronic wavelength.Thus,

and

Disclaimer:

I have created this blog for educational purpose,so for that i have written the content by referring many books,web pages.I have also uploaded google images and you tube videos for the better understanding of concept and I would also like to inform you that I am not responsible for the ads which are being posted in my blog.

 

Introduction to electronics:Part 1

Electronics:

Electronics is defined as the branch of science and technology which relates to the conduction of electricity through vacuum by electrons alone or through gases by electrons and ions.Basically electronics refers to the study of flow and control of electrons in vacuum,gases,semi conductors,conductors and the devices which uses these electrons.

To understand the concept of electronics,we need to study the basic structure of atom and its related concepts. 

                                                                                                                                                                     Atom is defined as the smallest particle of matter that possesses the  chemical properties of chemical element. Initially, the concept atom has evolved from the research on electricity.Electricity is a form of energy resulting from the existence of electric charge.Charge can be either positive or negative.The movement of these charged particles gives electric current. so by doing research on electricity, has motivated scientists to find out the concept of atom.

First Michael Faraday has the studied the passage of electricity through the liquid solutions . Then with this phenomena,the study of electrical nature of matter was made by J.J.Thomson .

J.J Thomson model:

He has focused his attention on the passage of electricity through gases.The studies made by Thomson on the electrical discharge through gases at low temperature established that atom composed of charged particles - electrons and protons.

He described his atomic model of an atom as a sphere of  completely positively charged matter in which electrons were embedded.His model could not explain all the properties of optical spectra of hydrogen and other elements.

Rutherford model:

In the year 1911, Rutherford has found that an atom consists of  a positively charged nucleus around which,the negative charged particles called electrons are moving by surrounding this central positive core. 

As a specific illustration of this model,let us consider a hydrogen atom.This simple hydrogen atom consists of a positively charged nucleus (a proton) and an electron.The charge of the proton is positive and is equal to the magnitude of electron.Therefore,an atom as a whole is electrically neutral.

Practically,as the proton carries the entire mass of the atom,it will substantially remain immobile,where as the electron will move about it in a closed orbit. Therefore,there exist a force of attraction between the proton and electron.This force of attraction between the proton and the electron,follows Coulomb's law.From the classical mechanics,the resultant closed path will be a circle or an ellipse under the action of such a force.Assume that the orbit of electron in the planetary model of an atom is a circle and the nucleus is supposed to be fixed in space.

Let us  calculate the radius of an electron in an orbit in terms of total energy(W) of the electron:

The force of attraction between the electron and nucleus is given by,
  
where,
the electronic charge e is in coulomb's
the seperation r between the two particles is in meters
force is in newtons
  is the permitivity of free space.

By Newton's second law of motion,this force of motion,this force must be set equal to the product of electronic mass 'm' in kilograms,electonic mass 'm' in kilograms and the acceleration towards the nucleus.Then
  ---------------> (1)

Further more,the potential energy of the electron at a distance 'r' from the nucleus is and the kinetic energy is given by . Then according to the law of conservation of energy,
-------------> eqn (2) where W is the energy in Joules.

Now, we can write eqn (1) as,

------------------------------> eqn(3)


substitute eqn (3) in eqn (2),we get


------------------------> eqn (4)
which gives the desired relationship between the radius and the energy of electron.

Eqn (4) shows that the total energy of electron is always negative.The negative sign arises because the potential energy has been chosen to zero when r is infinite.This expression also shows that the energy of electron becomes smaller as it approaches closer to the nucleus.

Rutherford model couldn't explain two points which are contradicting to what is normally happening in an atom:

1. If the accelerated electron loses energy by radiation,then the total energy of the electron continually decreases and it must spiral down into the nucleus.Then hydrogen atom cannot be stable,but most of the atoms are stable.

2.according to the classical electromagnetic theory,an accelerating electron must radiate energy at frequency equal to the mechanical frequency of orbiting electron and hence proportional to the angular velocity f the orbiting electron and hence proportional to the angular velocity of the electron. Therefore, as the electron spirals towards the nucleus,the angular velocity tends to infinity and hence frequency will also tend to infinity.This will result in a continuous spectrum with all possible wavelengths but many other atoms like hydrogen emit line spectra of fixed wavelength only.

Bohr's model:
Bohr model could successfully explain many of the atomic phenomena  which Rutherford model couldn't explain.Bohr took Rutherford model of an atom and tried to overcome the defects of the model. Bohr proposed the laws of classical mechanics and electromagnetic broke down within the atom.

The basic postulates of Bohr's theory are a combination of the ideas of classical theory and Planck's quantum theory of radiation.Bohr's postulates are as follows:

• Postulate 1:Not all energies as given by classical mechanics are possible,but the atom can possess only certain energies.While in states corresponding to discrete energies,the electron does not emit radiation,and the electron is said to be in a stationary or in a non-radiating state.
• Postulate 2:In a tranistion from one stationary state corresponding to a higher energy state to a lower energy state,with an associated energy W,radiation will be emitted.The frequency of this radiant energy will be given by,
• Postulate 3:Any stationary or non-radiating state is determined by the condition that is angular momentum of the electron in this state is quantized and must be integral mutiple of    .Thus 

Now, on combining these two with eqn (1) and (4) in rutherford model,we get,
 
   
For nth orbit,let the radius be    ,then,substitute the above equation in (1),







 -----> This equation represents the radius of electron in n th orbit.

To calculate the energy of the nth orbit,substitute the value of  in the equation(4) :





 ---------> This equation represents the total energy of an electron in nth orbit.

Atomic energy levels:

Though it is theoretically possible to calculate to calculate various energy states of the atom of simple elements,these levels must be determined indirectly for spectroscopic and other data for more complicated atoms.the experimentally determines energy level diagram for hydrogen is as shown below.,

fig., atomic energy levels of hydrogen atom

The lowest energy level (n=1) corresponds to normal unexcited state of hydrogen.This state is also called as ground state.In energy level diagram the lower energies(more negative) at the bottom while higher energies(less negative) are at the top.so it is easier to remove an electron from higher orbit than lower one.  By such a consideration,various electrons jumps between allowed orbits will be vertical arrows between the different  energy levels.The energy of radiated photon is greater when the length of the arrow is greater.The grater is the length of the arrow,higher is the frequency of emitted radiation. It is obvious from the figure that the various energy levels are separated  by forbidden energy gaps where the electrons cannot exist.

The photon nature of light:
In the transition process,the electron in an atom must lose an amount of energy equal to the difference of energy between the two states that is successively occupied.This energy appears in the form of radiation.According to Bohr's postulates,this energy is emitted in the form of photon of light.The term photon denotes the amount of radiant energy equal to the constant "h" times of the frequency.This quantized nature of an electromagnetic wave was first introduced by Planck in 1901,in order to theoretically verify black body radiation formula which is obtained experimentally.

The concept of photon radiation may be difficult to comprehend at first.Classically,it was believed that the atoms were systems that emitted radiation continuously in all directions.However it is not true from further concepts as the emission of light by an atom being a discontinuous process,so the atom is radiated only when the transition takes place from one energy level to another energy level.In this transition,it emits a definite amount of energy from one particular frequency,namely,one photon hf of light.





Disclaimer:
Dear viewers,I have created this blog for educational purpose,so for that i have written the content by referring many books,web pages and i have also uploaded google images,other websites and you tube videos,other website for the better understanding of concept and I would also like to inform you that I am not responsible for the ads which are being posted in my blog.