Modern Physics

Q1. What is matter wave?              Or  What is De­broglie hypothesis?

Ans: 1. According to de­broglie hypothesis, any moving particle is associatedwith a wave. 

2.  The  waves  associated  with  a  particle   is   called  matter  wave/de­brogliewave.

3.Wavelength   associated   with   the   matter   wave   is   called   de­brogliewavelength.                                        λ =               Or   λ =

           m= mass of the particle v= velocity of the particle p=mv= momentum of the particle.

Q2. Derive the expression for de-broglie wavelgth.

Ans:

                             

mvh h

p

E = hν=hc/ hv/ –-------1 E = mc2 = mv2 ---------------------2

1=2 hv/ = mv2.

Cancel v. h/ = mv since mv = p.

h/ = p

= h/p

Q3. Expression for de­broglie wavelgth in different forms

.

Q4. Write the properties of Matter waves.   

Q5:    Describe the Davission­Germer expriment  for the proof of wavenature of matter Or Describe the Davission­Germer expriment for the exprimental evidenceof matter waves.

Ans: 1. Experimental arrangement consist of filament, Ni crystal, detector.2.  Electron  beam (electrons)  are  generated  from  the  filament  by  passing  high currentthrough it. When filament gets heated up, it emits electrons.3. Emitted electrons are accelerated by  potential (voltage)  applied between filament andthe anode.4. Accelerated electron beam is allowed to fall on the Ni crystal. 5. These electrons are scattered by Ni crystal in all the directions.

6. The detector D measures the number of electrons scattered by the crystal in differentdirections/angles (0­90 degrees).7. Experiment was performed for different accelerated potentials .8. At 54V accelearting voltage, intensity graph have shown below. It is cleared that at 50degrees, a intense hump (intense peak) is observed.   This indicates that electrons arescattered more. This behaviour is not observed for other accelerating voltages.

9. If you calculate wave length associated with electrons at 54 V

                                                              = 1.66 Å------------------------1

10. From below figure, we can measure angle of incidence of electron beamon the Ni crystal planes and it is found that 65 degrees.

Or

11. Substitute above values in braggs law of x-ray diffraction

According to braggs law 2dsinθ=nλ

d=0.91 Å, n=1, θ=65o

λ= 1.65 Å ------------------------2

12. from the values of wavelength obtianed by equation 1 (De-broglie) and 2 (braggs) are same/agreed well.

Ф

Ф

At 54 V

Intensity Peak /hump

Ф=50O

13. Therefore, this experiment gave a evidence that electrons exhibit diffraction (wave nature). This implies the existance of matter waves.

Q6:  Describe the G P Thomson's expriment for the proof of wave natureof matter Or Describe the G P Thomson's expriment for the exprimental evidence ofmatter waves.

Ans: 1. Experimental arrangment consist of Filament (F), Anode (A), Photograhic plate (P), Thin gold foil (G) (Poly crystalline) and Metal block (B).

2. Electrons are produced from the heated filament (F) and accelerated through highpotentail given to the anode (A).

3. Electron beam passes through a fine hole in metal block (B) and falls on the goldfoil of thickness 0.1 μm. The electron are passing through foils are received on thephotographic plate (P).

4. Metals are poly crystalline in which grains are oriented randomaly and somegrains always satisfies braggs law with respect to the incident electron beam angleand produce the braggs reflection.

5. A concentric ring pattern is produced on the photographic plate like as shown inbelow.

6. X-ray diffraction pattern of powder (poly crystalline) samples is shown in below.

Form above two figures, the diffraction pattern produced by electron beam is similarto the x-ray diffraction pattern produced using x-rays.

Therefore, this experiment provides the evidence for the wave nature of electron.Which implies the existance/evidence of matter waves.

Q7. Explain the terms (a) Wave packet (b) Group velocity (c) Phasevelocity.

Ans:

(a) Wavepacket: It is representation of matter wave associated with aparticle. Which is represnted bleow

                                      

Wave packet is the   resultant of superpostion of large number of harmonicwaves slightly differ in frequency

(b)  Group  velocity   (Vg):  The  velocity  with  which  wave  packet   advances(moving) in the medium is called group velocity.                                                                                    Vg =                                               

dω

dk

(c) Phase velocity (Vp): The individual waves forming the wave packetpropogate at a velocity known as the phase velocity (Vp)

                                    Vp= ω/k

Q8.     What   is   Heisenberge   uncertainity     principle   and   write   itsapplications

Ans:  Principle: It is impossible to measure both the position and momentum of  aparticle simulataneously and precisely. 

                                       Δp Δx≥

h4 π

                      Other forms  ΔE Δt≥h

4 π 

Application 1

Application 2 

Application 3  Particle in a box : Let us consider  a particle confined to a box of length l.The uncertainity  Δx in the position is l 

Δx .ΔP ≈ h ( h cut/h bar)

ΔP=h/l ( Δx=l )

E= P2/2m

E= (ΔP)2/2m

 E= h2/2ml

      This  Energy result agrees with the result obtained from the schrodingerwave equation .                        

Q9.       Derive   the  Schrodinger’s time independent waveequation.

Ans: 

Q 10 Write physical significance of wave function.

Ans:

1. It gives a statistical relationship between the particle and wave.

2.

3. 

4. 

The probability of finding a particle within a volume dv

P= ∫ ΨΨ* dv= ∫ |Ψ|2dv

dv=dxdydz, Ψ2 Gives the probability finding a particle.

When the particle definately exist in a volume

P= ∫ ΨΨ* dv=1 (Normalization condition )

When the particle does not exist in a volume

P= ∫ ΨΨ* dv=0

Q11. Derive Schrodinger Equation for a particle in a one dimensional "box" and find its energy (eigen ) values, wave (eigen) functions and probability.

Q.12 Explain the formation of energy bands in solids

Q.13 Distingush between insulator, conductor, and semiconductor.

1. Conductors

2. Semiconductors

3. Insulator

Q. 14 Explain in detail the comparison among Maxwell Boltzmen (M-B), Fermi Dirac (F-D) and Bose-Einstein (B-E) statistics

Q . 15 Define the tunneling phenomenon and find the transmission and reflection coefficient of the partcile (electron) in case of rectangular potential barrier.

OrExplain the tunneling phenomenon in case of rectangular potential barrier.

Ans: Defination : Quantum tunnelling or tunneling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not not possible like as shown in the figure.

Rectangular potential barrier:

V(x)=V0

V=0 V=0

X=0 X=L

Region - I Region -II Region -III

The-end