N AND P TYPE SEMICONDUCTORS

N-TYPE SEMICONDUCTORS: -

N-type semiconductors is prepared by adding pentavalent impurities like Antimony or Arsenic in pure semiconductor. P-type semiconductor is prepared by adding trivalent impurities like Aluminium, Gallium or Indium.
The figure shows N-type semiconductor in which two Arsenic atoms have replaced two Germanium atoms in the lattice structure of Ge crystal. Four of the five valence electrons of As atom are used up in forming covalent bonds and the fifth electron can act as a free electron with 0.01 eV energy. This energy is 0.05 eV in case of Silicon atom. This much energy is easily available at room temperature as thermal energy.

The pentavalent impurity is called donor impurity as it denotes the electric charge carrier electron, to the host atom. It is added in proportion of 1 in 106 pure atoms. Hence in one mole of crystal, about 1017 impurity atoms and 1017 free electrons are present. A good conductor like copper contains nearly 1023 free electrons per mole. Besides these, some more free electrons and equal number of holes result from breaking of covalent bonds. As their number is very small as compared to the free electrons from the impurity atoms, electrons are the majority charge carriers and holes minority charge carriers in the case of N-type semiconductors ( n e > n h ).

P-TYPE SEMICONDUCTORS: -

If trivalent impurities like Aluminum is
added to Ge or Si, then three free electrons of this impurity atom form covalent bonds with its neighbouring three Ge or Si atoms. Thus there is a deficiency of one electron in the formation of the fourth covalent bond. This deficiency of electron can
considered as a hole which is present in one of the bonds between the aluminium and Ge or Si atoms. This hole has a tendency to attract electron. Hence aluminium atom is known as acceptor impurity. Here, holes which behave as positively charged particles are majority charge carriers and electrons are minority charge carriers. Hence such a semiconductor is known as P-type semiconductors  (n e > n h). The figure shows symbolic representation of aluminium impurity added to Ge crystal lattice.

CONDUCTORS, INSULATORS AND INTRINSIC SEMICONDUCTOR

The elements in the first three groups of the periodic table like alkali metals, noble metals, Aluminum, etc. are good conductors due to the presence of free electrons. Non-metals are bad conductors of electricity due to lack of free electrons. The elements in the fourth group of the periodic table like Si and Ge have greater resistance than good conductors but less than bad conductors. They are known as semiconductors. They behave as bad conductors at absolute zero temperature in their pure form.

The resistivity of the good conductors increases with temperature, while the resistivity of the semiconductors decreases on increasing the temperature unto a certain limit. The conductivity of the semiconductors is changed by making radiation of suitable frequency incident on them.

Two very important semiconductors Ge and Si are discussed here. Both have diamond crystal structure. If an atom of Si is considered at the center of the tetrahedron, then its four nearest neighbours are at the vertices's of a tetrahedron as shown in the figure. Diamond crystalline structure is obtained on extending this arrangement in a three dimensional space.

The electronic arrangement of Si is 1s² 2s² 2p⁶ 3s² 3p². The electrons in 1s² 2s² 2p⁶ completely occupy the K and L shells. 3s² 3p² electrons are the valence electrons. These 2 s orbitals and 2 p orbitals combine to form 4 sp³ complex orbitals. These orbitals combine with similar such orbital’s of the neighbouring atoms and form covalent bonds. Thus, each of the four valence electrons of the silicon forms a covalent bond with its four neighbouring atoms as shown in the figure.

At absolute zero temperature, Si and Ge behave as insulators as the valence electrons are bound in covalent bonds. At room temperature, these bonds break due to thermal oscillations of atoms freeing the electrons which increase conductivity. Deficiency of electron in a bond produces a vacant space which is known as a hole. The hole has the ability of attracting electrons and the randomly moving free electron can get trapped in a hole. Thus hole behaves as a positive charge though it is neither a real particle nor has any positive charge.

On applying p.d. between two ends of a crystal as shown in the figure, electric current gets set up. Now, thermal oscillations and external electric field cause covalent bonds to break and the free electrons produced get trapped in the holes during their motion. Simultaneously, new holes are produced by electrons breaking free from the covalent bonds. The free electrons move towards the positive end and the holes to the negative end. The motion of holes towards the negative end is equivalent to the motion of bound electrons towards the positive end. Thus current in a semiconductor is due to ( i ) motion of free electrons and ( ii ) motion of bound electrons. Both these currents are in the same direction.

The number density of free electrons n_e and holes n_h in a pure semiconductor are equal. Pure semiconductor is called intrinsic semiconductor. Hence electrons and holes are called intrinsic charge carriers and their number density is indicated by n_i. n_e = n_h = n_i.

BEATS

DEFINITION: -

"Beats can be defined as the periodic variation in the intensity of sound at a given point

due to super-position of two waves having slightly different frequencies."

EXPLANATION: - 

When two waves having slight difference of frequency and same amplitude pass through the same region of space, interference takes place. This type of interference is known as 'Beats'. In this case when two waves are observed at a given point they are periodically in or not of step with one another. That is, there is an alternation in time b/w constructive and destructive interference. This alternation is called Beats

EXPLANATION WITH EXAMPLE: -

If two tuning forks of slightly different frequencies are set to vibrate simultaneously, we hear a sound of alternating high and low intensity. This is called a beat and phenomenon is called is Beats.

BEAT FREQUENCY: -

Beat frequency is the no. Of beats one hears in one second. It is defined as the difference infrequency b/w two sounds.

The maximum beat frequency that a human ear can detect is 7beats/seconds.

ULTRASONICS: -

Definition: -

The longitudinal waves with frequencies above the audible range are known as ULTRASONICS. Ultrasonic have frequency greater than 20,000Hz.

PRODUCTION OF ULTRASONICS: -

Ultrasonic are produced by vibrating quartz crystals electricity. With the help of this device very high frequency range ultrasonic waves can easily be produced.

USES OF ULTRASONICS IN MEDICINE: -

·         Ultrasonic is now widely used as diagnostic therapeutic and surgical tool in medicine.

·         Ultrasonic is preferred over x-rays due to safety.

·         To kill microbes in liquids.

IN INDUSTRY: -

·         To find cracks in metal structures.

IN TECHNOLOGY: -

·         They are used in echo-depth sounding devices for determining depth of sea.

·         In under water navigation ultrasonic is used instead of RADAR.

IN GENERAL: -

·         In guidance devices for blind persons.

SECOND'S PENDULUM: -

A pendulum that completes its one vibration is two seconds is known as 2nd’s pendulum.

Or

A pendulum whose time period is 2 sec is called second's pendulum.

·         Frequency of second pendulum is 0.5Hz

·         Length of second's pendulum is 100cm.

CHARACTERISTICS OF SOUNDS

Musical sound has the following characteristics:

1.      Loudness

2.      Pitch

3.      Quality or Timber 

LOUDNESS OF SOUND: - 

Definition: -

Loudness is that characteristics of musical sound which enables us to distinguish between a faint sound and a loud sound.

OR

Loudness is defined as the auditory sensation produced by the sound in ear.

Loudness of sound depends upon the intensity of sound. Loudness is actually a sensation of human consciousness. It is denoted by 'L'.

Loudness of sound is directly proportional to the logarithm of the intensity of sound

i.e.

L ∞ Log I

L = K (Log I)

Where "I" is the intensity of sound.

FACTORS ON WHICH LOUDNESS DEPENDS: - 

Area of vibrating body: -

The larger the area of vibrating body the louder the sound produced. For example a DHOOL produces a loud sound due to larger area. Similarly a small DHOLAC or CONGO produces a small loudness.

Amplitude of vibrating body:

The greater the amplitude of vibrating body, the louder the sound produced.

Distance b/w source and listener:

Smaller is the distance b/w source of sound and the listener greater is the loudness of sound as heard by the listener.

 PITCH OF SOUND: -

"The characteristic of sound by which a shrill sound can be distinguished from a grave sound is known as PITCH."

Pitch of sound depends upon the frequency of sound. The greater the frequency, the higher is the pitch and vice versa. It is the pitch of sounds that enable us to distinguished b/w a sound of man and woman or man and dog. Etc. sound of a woman is shrill due to high pitch. Sound of a dog is grave due to low pitch and low frequency.

QUALITY OR TIMBER: -

"The property of sound by virtue of which we can distinguish between two sounds of the Same pitch and the loudness originating from two different musical instruments."

The sound produced by two different instruments is usually complex. It is a mixture of several tones. The tone of lowest frequency is called Fundamental frequency and other tones are known as OVERTONES OR HARMONICS. The loudness of sound depends upon the amplitude of vibration. And pitch determined by its fundamental frequency. Two or more sound may have the same loudness and the same pitch but that they may differ in number and relative intensities of overtones. The quality of sound depends upon the wave form of the resultants. Nature has such a great diversity that it is very rare to have some overtones of two persons exactly. So this difference is overtones make it possible to recognize each sound. This characteristic of sound is called QUALITY.

INTENSITY OF SOUND: -

"The intensity of sound is defined as the amount of energy transmitted per second through unit area held perpendicularly in the direction of sound waves."

Intensity of sound = E / t. A

OR

I = E / t. A

Unit:

        In international system the unit is  Watt / m² 

STANDING WAVES

When two identical progressive waves with sane amplitude and frequency travel through a medium with equal velocity in opposite direction, they super impose over each other and produce a new type of wave which is known as Stationary Wave or Standing Wave.

In stationary waves there is no flow of energy along the waves.

When stationary waves are set up in a medium, the medium vibrates in several segments called Loops.

The point of destructive interference is called NODE, at nodes displacement is zero.

The point of constructive interference is called anti nodes; at anti node displacement is maximum.

INTERFERENCE

When two waves pass through a medium at a point, then the resultant displacement at that point is the vector sum of the displacements due to two component waves. This modification in displacement as a result of superposition of two waves is called INTERFERENCE.

The phenomenon in which two waves traveling in same direction reinforce each other at some points and cancel the effect of each other at some different points is called Interference of waves.

CONSTRUCTIVE INTERFERNCE: -

Type of interference in which two waves overlap each other in such a way that they reinforce or increase the effect of each other is called Constructive Interference.

In constructive interference crest of one wave coincides that crests of other and trough coincides with trough.

In constructive interference path difference of two waves is 'm λ’

DESTRUCTIVE INTERFERENCE: -

Type of interference in which two waves overlap each other in such a way that they cancel the effect of each other is called Destructive Interference.

In destructive interference crest on wave coincides the trough the other wave.

In destructive interference path difference of two waves is (m + ½) λ.

WAVE MOTION

The mechanism by which energy travels (transfers) from one point to the other point is called as Wave Motion. Wave motion is one of the most important ways of transferring energy.

A wave motion may be defined as a disturbance which travel in the material medium and carry energy.

LONGITUDINAL WAVES: -

The type of wave motion in which particles of medium vibrates to and fro and execute S.H.M. in the direction of propagation of waves is called Longitudinal Wave.

A longitudinal wave is one in which the disturbance of medium particles in parallel to the direction of travel of the wave. 

EXAMPLES: -

Sounds waves, waves, set-up in spring.

TRANSVERSE WAVES: -

The type of motion in which particles of medium vibrate to and fro or execute S.H.M. in the direction perpendicular to the direction of propagation of waves is called Transverse Waves.

EXAMPLES: -

Light waves, radio waves, microwaves

RIPPLE TANK

INTRODUCTION: -

 RIPPLE TANK is an apparatus which is used to study the features or characteristics of wave’s mechanics.

CONSTRUCTION: -

A ripple tank consists of a rectangular tray containing water. It is provided with a transparent glass sheet at the bottom. A screen is placed well below the tray to observe the characteristics of waves generated in water. A lamp is placed above the tray

WORKING: -   

When an observer dips a rod or his finger into the water of ripple tank, waves are generated. There is also a mechanical way to generate pulses in water i.e. electric motor. The lamp enlightens the waves which are focused on the bottom screen. The wave crests act as converging lenses and tend to focus the light from the lamp. The wave troughs act as diverging lenses and tend to spread it. This results that crests appear as bright bends and troughs as dark bends on the screen.

PRODUCTION OF STRAIGHT RIPPLES: -

 Straight pulses are produced by dipping a finger or a straight rod periodically in water.

PRODUCTION OF CIRCULAR RIPPLES: -  

Circular pulses are produced by dipping the pointed end of a rod periodically in water.

ANALYSIS OF WAVES: -

If straight pulses are generated and a piece of paper is thrown on the surface of water, it is found that the paper simply moves up and down as each of the waves passes across it. By means of a stop watch time period of the rod and paper is measured. The two time periods are found to be equal. This shows that the particles of medium execute simple harmonic motion with the same time period as that of the body generating pulses.

SIMPLE PENDULUM

Simple pendulum consists of a heavy mass particle suspended by a light, flexible and in-extensible string.

MOTION OF THE BOB OF SIMPLE PENDULUM: -

The motion of the bob of simple pendulum, simple harmonic motion if it is given small displacement. In order to prove this fact considers a simple pendulum having a bob of mass 'm' and the length of pendulum is 'l'. Assuming that the mass of the string as pendulum is negligible. When the pendulum is at rest at position 'A', the only force acting is its weight and tension in the string. When it is displaced from its mean position to another new position say 'B' and released, it vibrates to and fro around its mean position.

   Suppose that at this instant the bob is at point 'B' as shown below:

FORCES ACTING ON THE BOB   : -

·         Weight of the bob (W) acting vertically downward.

·         Tension in the string (T) acting along the string.

The weight of the bob can be resolved into two rectangular components:

1.      W cos θ along the string.

2.      W sin θ perpendicular to string.

  Since there is no motion along the string, therefore, the component W cos θ must balance tension (T)

i.e.                                                                      W cos θ = T

  This shows that only W sin θ is the net force which is responsible for the acceleration in the bob of pendulum.

  According to Newton's second law of motion W sin θ will be equal to m × a

  i.e.                                                                      W sin θ = m a

  Since W sin θ is towards the mean position, therefore, it must have a negative sign.

i.e.                                                                     m a = -  W sin θ 

But W = mg

                                                                         m a = -  m g sin θ 

                                                                               a = - g sin θ  

In our assumption q is very small because displacement is small, in this condition we can take sinθ = θ

Hence                                                                     a = - g θ ----------- (1) 

If x be the linear displacement of the bob from its mean position, then from figure, the length of arc AB is nearly equal to x 

From elementary geometry we know that:

Where s = x, r = l

Putting the value of q in equation (1)

 As the acceleration of the bob of simple pendulum is directly proportional to displacement and is directed towards the mean position, therefore the motion of the bob is simple harmonic when it is given a small displacement.

Show that the motion of a mass attached to the end of a spring is SHM: -  

 

Consider a mass "m" attached to the end of an elastic spring. The other end of the spring is fixed at the firm support as shown in figure "a". The whole system is placed on a smooth horizontal surface. If we displace the mass 'm' from its mean position 'O' to point "a" by applying an external force, it is displaced by '+x' to its right, there will be elastic restring force on the mass equal to F in the left side which is applied by the spring.

 According to "Hook's Law 

F = - K x ---- (1)

   Negative sign indicates that the elastic restoring force is opposite to the displacement.

   Where K= Spring Constant

If we release mass 'm' at point 'a', it moves forward to ' O'. At point ' O' it will not stop but moves    forward towards point "b" due to inertia and covers the same displacement -x. At point 'b' once again elastic restoring force 'F' acts upon it but now in the right side. In this way it continues its motion from a to b and then b to a.

According to Newton's 2nd law of motion, force 'F' produces acceleration 'a' in the body which is given    by

F = m a ---- (2)

Comparing equation (1) & (2)

m a = - k x

Here k / m is constant term, therefore,

a = - (Constant) x

or

a ∞ -x

   This relation indicates that the acceleration of body attached to the end elastic spring is directly    proportional to its displacement. Therefore its motion is Simple Harmonic Motion.

SIMPLE HARMONIC MOTION

"Type of vibratory motion in which acceleration of body is directly proportional its displacement and the acceleration is always directed towards the equilibrium (mean) position is called Simple Harmonic Motion. "

Acceleration ∞- displacement

a ∞ - x

Negative sign indicates that acceleration and displacement are opposite in direction.

Examples of S.H.M:

BASIC CONDITIONS TO EXECUTE SHM: -

Basic conditions to execute simple harmonic motion are as under:

·         There must be elastic restoring force acting on the system.

·         The system must have inertia.

·         The acceleration of the system should be directly proportional to its displacement and is always       directed to mean position i.e. a ∞ - x 

   

EXAMPLES OF SHM: -

·         Motion of a body attached to the end of an elastic spring

·         Motion of the bob as a simple pendulum if it is gives a small displacement.

Motion of an elastic strip.

·         Motion of the prongs of a tuning fork.

·         Motion of the wire of a guitar or violin.

CHARACTERISTICS OF SHM: -

·         The motion must be vibratory.

·         The motion should be a periodic motion.

·         The restoring force should be directly proportional to the displacement of the body from its mean position.

RADIOACTIVITY, PROPERTIES OF RADIOACTIVE RAYS

RADIOACTIVITY
All the elements having atomic number greater than 82 emit invisible radiation all the time. The phenomenon of emission of these powerful rays is called "Natural Radioactivity" and the element that emits such rays is called "Radio Active Element".
TYPES OF RADIO ACTIVE RAYS
There are three types of radioactive rays: ·         α-Rays  ·         β-Rays ·         γ-Rays
·         PROPERTIES OF α-RAYS: -
(a) NATURE: α ray consists of α particle. Each α particle consists of Helium (2He4) nucleus.
(b) CHARGE: α particle carry positive charge.
(c) MASS: Mass of each α - particle is 4 times that of a proton or H-atom.
(d) IONIZATION: Ionization power of α ray is very high.
(e) PENETRATION POWER: Penetration power of α ray is very small.
(f) FLUORESCENCE: α ray’s produce fluorescence in different substances.
(g) EFFECT ON HUMAN BODY: α ray produce burn and sore on human body.
(h) ARTIFICIAL RADIO ACTIVITY: α rays can produce artificial radioactivity is certain nuclei.
·         PROPERTIES OF β –RAYS: -
(a) NATURE: β rays consist of fast moving electrons.
(b) CHARGE: β rays have negative charge.
(c) VELOCITY: Velocity of β rays is from 9 x 107 m/sec to 27 x 107 m/sec.
(d) EFFECT ON PHOTO GRAPHIC PLATE:  β rays affect photo graphic plate
(e) IONIZATION POWER: Ionization power of β rays is very small.
(f) KINETIC ENERGY: Kinetic energy of β rays is less than that of β - rays.
(g) FLUORESCENCE: β rays produce fluorescence in different substance.
·         PROPERTIES OF γ – RAYS: -
(a) NATURE: γ rays are electromagnetic radiation.
(b) CHARGE: γ - rays are no charge.
(c) VELOCITY: γ - rays travel with the velocity of light that is 3 x 108 m/sec.
(d) PENETRATION POWER: Penetration power of γ - rays is very large. It is about hundred times larger than that of γ rays.
(e) FLUORESCENCE: γ - rays produce feeble fluorescence When incident on screen coated with barium platino cyanide.