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Handbook of Particle Physics - J. Sundaresan

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 Book Description

 This unique work contains, in encyclopedic form, terms of interest in particle physics, including its peculiar jargon. It covers the experimental and theoretical techniques of particle physics along with terms from the closely related fields of astrophysics and cosmology. Designed primarily for non-specialists with a basic knowledge of quantum mechanics and relativity, the entries preserve a degree of rigor by providing the relevant technical and mathematical details.

Clear and engaging prose, numerous figures, and historical overviews complement the handbook's convenience both as a reference and as an invitation into the fascinating world of particle physics

What should be the lengths of an aluminium and a brass rods at STP.so that brass rod is longer than the aluminium rod by 4cm at all conditions of temperature.(alpha alumn 24exp -6 brass 20 expo -6c


Data :

Let
Length of aluminum = La
Length of brass = Lb =La + 0.04 (In meters)
α for aluminum= 24x10 -6 c-1
α for brass= 20 x10 -6 c-1
Lengths at 0 0C La’ = ? and Lb’=?

Solution:

 Length of aluminum is given by
La’=La ( 1 + α Δt)----------------1
Lb’=Lb ( 1 + α Δt)-----------------2
Subtracting eq(1) from eq(2), we get
La’ - Lb’ =La ( 1 + α Δt) - Lb ( 1 + α Δt)
              = La + La α Δt) - Lb + Lb α Δt
              =(La – Lb )+ Δt (La α - Lb α)
       0.04 =0.04 + Δt (La α - Lb α)
So Δt (La α - Lb α) =0
Since La α = Lb α
La x 24x10 -6 = Lb x20 x10 -6
La =(20 /24) x Lb =20 Lb / 24 ------------3
Since Lb =La + 0.04
Putting value of La from eq (3) , we get
Lb =(20 Lb / 24) +0.04  or 24 x (Lb -0.04)=20 Lb
24 Lb – 20 Lb =0.96   or Lb= 0.96/4 =Lb=0.24 m Answer
Now La= 0.24 -0.04 =0.02 m Answer
 

A x.ray photon of wavelength 1.82 exponent-10m is scattered at angle θ.if fractional change in wavelength is 2% then what is value of scattering angle?



A x.ray photon of wavelength 1.82 exponent-10m is scattered at angle θ.if fractional change in wavelength is 2% then what is value of scattering angle?

Data:
λ = 1.82 x 10 -10 m
Δ λ / λ = 2%
θ = ?

Solution:
According to Compton’s Shift we can write as
Δ λ =(h / mo c) ( 1- Cos θ) ----------(1)
Finding Δ λ
Δ λ = 2 % x  λ
Δ λ = 2 /100 x 1.82 x 10 -10 =   3.64 x 10 -12   m
Now using equation (1)
 1- Cos θ = Δ λ x mo c /h
or
Cos θ = 1- (Δ λ x mo c /h) = 1 – (3.64 x 10 -12  x 3 x 10 8 x 9.1 x 10 -31 / 6.63 x 10 -34)=-0.4988
Or
θ=Cos-1 (-0.4988) =120 0 Answer

COMMON EMITTER CONFIGURATION OF A TRANSISTOR


COMMON EMITTER CONNECTION




In this configuration, the input is applied between the base and the emitter and the output is taken from the collector and the emitter. In this connection, the emitter is common to both the input and the output circuits as shown in Fig. In the common emitter configuration the input current is the base current IB and the output current is the collector current IC. The ratio of change in collector current to the change in base current at constant collector-emitter voltage is called base current amplification factor ( ).

COMMON EMITTER CIRCUIT

A test circuit for determining the static characteristic of an NPN transistor is shown in Fig In this circuit emitter is common to both input and output circuits. To measure the base and collector current milli ammeters are connected in series with the base and the output circuits. Voltmeters are connected across the input and the output circuits to measure VBE and VCE There are two potentiometers R1 and R2 to vary the supply voltages VCC and VBB.

              Circuit arrangement to determine static characteristic of common emitter
                             
Input Characteristics

It is a curve which shows the relationship between base current IB and the emitter-base voltage, VBE at constant VCE. The method of determining the characteristic is as follows.



                                                Common emitter input characteristic curve

First, by means of R1 suitable voltage is applied from VCC, Next, voltage VBE is increased in number of steps and corresponding values of IB are noted. The base current is taken on the Y-axis and the base-emitter voltage is taken on the X-axis.

Fig shows the input characteristic for common emitter configuration. The following points may be noted from the characteristic.

1. The input resistance of the transistor is equal to the reciprocal of the slope of the input characteristic curve.


2. The initial portion of the curve is not linear.

3. The input resistance varies considerable from a value 4 kilo ohm to a value of 600 ohms.

4. In the case of silicon transistor the curves break away from zero current for voltage in the range of 0.5 to  0.6 volt whereas for germanium transistor the break away point is in the range 0.1 to 0.2V


Output Characteristics

It is a curve which shows the relationship between the collector IC and the collector- emitter voltage VCE. This method of determining the characteristic is as follows.

First by means of R1 a suitable base current IB is maintained. Next VCE is increased from zero, in a number of steps and corresponding values of IC are noted. The above whole procedure isrepeated for different values of IB. The collector current is taken on the Y-axis. Fig shows the family of output characteristics at different base current values. The following points may be noted from the family of characteristic curves.


                                      Common emitter characteristic curve


1.The collector current IC increases rapidly to a saturation level for fixed value of IB. But at the same time VCE increases from zero.

2.A small amount of collector current flows even when IB=0 the current is called ICEO. Now main collector current is zero and the transistor is cut-off.

3.The output characteristics may be divided into three regions.

The active region
Cut-off region
Saturation region

Active region: In this region the collector is reverse biased and the emitter is forward biased. The collector current, IC response is most sensitive for changes in IB. Since = /(1- ) and also is very close to unity. (I - ) is very small. Therefore, a slight change in a produces very large change in b and so the collector current,


is changed substantially

Cut-off region: When IE= 0 and IC = ICO, the cut-off condition of the transistor is reached. It is necessary that emitter junction has to reverse biased slightly i.e., 0.1 V for germanium and 0 volt for silicon.

In this region

Saturation region: In this region incremental change, in IB do not produce corresponding large changes in IC. The region is also refer to as bottomed region because the voltage has fallen near the bottom of the characteristic. In this configuration saturation is entered while collector is still reverse biased.

COMMON BASE CONFIGURATION OF A TRANSISTOR

COMMON BASE CONNECTION
In this configuration the input is applied between the emitter and base and the output is taken from the collector and the base. Here the base is common to both the input and the output circuits as shown in Fig.





In a common base configuration, the input current is the emitter current. and the output current is the collector current I The ratio of change in collector



current to the change in emitter current at constant collector-base voltage is called current amplification factor,


In a transistor VEB, IE, VCB, and IC are parameters.

  • These parameters can be interrelated in a number of ways. In these parameters the input current and the output voltage are taken as independent variables.
  • The input voltage and output current are then expressed in terms of these independent variables. And these dependent variables also be expressed in functional relationship.

                                                              i.e., VBE= f1 (IE,VCB)

                                                              IC= f2(In, VCB)

  • Thus the characteristics of a transistor is completely desired by the above two equations. These relationships can be conveniently displaced graphically.

  • The curves thus obtained are known as the static characteristics. The most important static characteristics are the input and the output characteristics

COMMON BASE CIRCUIT


  • A test circuit for determining the static characteristic of an NPN transistor is shown in Fig In this circuit, base is common to both the input and the output circuits.


  • To measure the emitter and the collector currents mull ammeters are connected in series with the emitter and the collector circuits.


  • Voltmeters are connected across the input and the output circuits to measure VBE and VCB There are two potentiometers R1 and R2 to vary the supply voltages VCC and VBE.



  • It is a curve, which shows the relationship between the emitter current, I and emitter-base voltage V at constant collector-base voltage V This method of determining the characteristic is as follows.




  • First by means of R1, a suitable voltage is applied to VCB from VCC. Next, voltages VBE is increased in a number of steps and corresponding values of IE are noted.


  • The emitter current is taken on the Y-axis and the emitter base voltage is taken on the X-axis. Fig 2.12 shows the input characteristic for germanium and silicon transistors.


The following points may be noted from the characteristics curves.

1.This characteristic may be used to find the input resistance of a transistor.The input resistance (ri) value is    given by the reciprocal of the input characteristic curve.

2.The emitter current IE increases rapidly with small increase in emitter- base voltage. It means that the input resistance is very high.

3.The emitter current is dependent of collector voltage.

OUTPUT CHARACTERISTICS

  • It is a curve which shows the relationship between the collector current IC and the collector-base voltage VCB at constant emitter current IE. This method of determining the characteristic is as follows.

  • First, by means of R2 a suitable voltage is applied to the base and the emitter. Next, VCB is increased from zero in a number of steps and corresponding values of IC are noted.

  • The above whole procedure is repeated for different values of IE for obtaining family of curves.

  • The collector-base voltage is taken the X-axis. Fig shows the family of output characteristics at different emitter current values.

  • The following points may be noted from the family of characteristic curves.





  • The collector current IC varies with VCB only at very low voltages.

  • This characteristic may be used to find the output resistance (rO)


  • A very large change in collector-base voltage produces small change in collector current. It means that the output resistance is very high.

  • The collector current is constant above certain values of collector-base voltage. It means that IC is independent of VCB and depends upon IE only.

The output characteristics may be divided into three regions

1. The active region

2. Cut-off region

3. Saturation region

Active region: In this region the collector junction is reverse biased and the emitter junction is forward biased. In this region when IE= 0, IC = ICO. This reverse saturation current remains constant and is independent of collector voltage V as long as is below the break down potential. When emitter current flows in the emitter circuit then a fraction (- IE) of this current reaches the collector. Hence IC = - IE + ICO. Thus in the active region the collector current is independent of collector voltage and depends only upon the emitter current. But due to Early effect there is a small increase (0.5%) in IC with increase in VCB

Saturation region: The region to the left of the ordinate VCB = 0 is called the saturation region. In this region both junctions are forward biased. This is also called as bottomed region because the voltage has a fallen near the bottom of the characteristic where VCB = 0. In this region IC increases rapidly with even small increase VCB in as shown in Fig

Cut-off region: The region below the IE= 0 characteristic, for which the emitter and collector junction are both reverse biased, is called cut-off region. This portion of characteristic is not coincident with the voltage axis as shown in Fig.

COMMON COLLECTOR CONFIGURATION OF A TRANSISTOR

COMMON COLLECTOR CONNECTION

In  this  configuration  the  input  is  applied  between the  base  and  the  collector and  the  output  is  taken  from  the  collector  and  the  emitter.  Here  the  collector  is common to both the input and the output circuits as shown in Fig.

                                                       Common Collector Transistor Circuit

In  common  collector  configuration  the  input  current  is  the  base current  IB  and  the output current is the emitter current IE. The ratio of change in emitter current to the  change in the base current is called current amplification factor.

It is represented by


COMMON COLLECTOR CIRCUIT

A test  circuit  for determining the  static characteristic  of an NPN transistor is shown in Fig. In this circuit the collector is common to both the input and the output circuits.   To   measure   the   base   and   the   emitter   currents,   milli   ammeters   are connected in series with the base and the emitter circuits. Voltmeters are connected   across the input and the output circuits to measure VCE and VCB

INPUT CHARACTERISTICS

                                                Common Collector Input Characteristic Curve


  • It  is  a  curve  which  shows the  relationship  between the  base  current,  IB and the collector base voltage VCB at constant VCE This method of determining the characteristic is as follows.

  • First, a suitable voltage is applied between the emitter and the collector. Nextthe  input  voltage  VCB  is  increased  in  a  number  of  steps  and  corresponding values of IE are noted.

  • The base current is taken on the y-axis, and the input voltage is taken on the x-axis. Fig. shows the family of the input characteristic at different collector- emitter voltages.

  • The following points may be noted from the family of characteristic curves.  1.Its  characteristic  is  quite  different  from  those  of  common  base  andcommon emitter circuits.
2.When VCB increases, IB is decreased.

Output Characteristics

  • It is a curve which shows the relationship between the emitter current l and collector-emitter voltage, the method of determining the output characteristic is as follows.

  • First,  by  adjusting  the  input  a  suitable  current  IB  is  maintained.  Next  VCB increased in a number of steps from zero and corresponding values of IE are  noted.

  • The above whole procedure is repeated for different values of IB. The emitter current  is  taken  on  the  Y-axis  and  the  collector-emitter  voltage is  taken  on the X-axis.

  • Fig shows the family of output characteristics at different base current values. The following points are noted from the family of characteristic curves.
                                         Common Collector Output Characteristic Curves

1.This  characteristic  is  practically  identical  to  that   of  the  common  emitter circuit.

2.Its current gain characteristic for different values of VCE is also similar to that of a common emitter circuit.

Thermal physics - Kittel

 



Book Description

For upper-division courses in thermodynamics or statistical mechanics, Kittel and Kroemer offers a modern approach to thermal physics that is based on the idea that all physical systems can be described in terms of their discrete quantum states, rather than drawing on 19th-century classical mechanics concepts.

Q. The matrices representing the angular momentum components jx jy jz are all hermitian .Show that the Eigen values of j2 is equal TO J2 =JX2 +JY2+JZ2 are REAL AND NON-NEGATIVE.


 Ans. This question is taken from the "Mathematical Methods for Physicist" Problem number 3.5 from chapter no 3

Finding the eigen values for J2=Jx2 + Jy2 + Jz2
Then we get
(Jm |J2|Jm)= (Jm |Jx2|Jm) +(Jm |Jy2|Jm)+ (Jm |Jz2|Jm)
Which can also be written as
|Jx(jm)|2 + |Jy(jm)|2 + |Jz(jm)|2
The above equation shows that the eigen values for J2=Jx2 + Jy2 + Jz2 are real and non negative
 
 for complete understanding download and See Chapter 3 page no. 19

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