modern physics - wordpress.com · 2016. 10. 20. · modern physics q1. what is matter wave? or what...
TRANSCRIPT
![Page 1: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/1.jpg)
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
![Page 2: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/2.jpg)
Q3. Expression for debroglie wavelgth in different forms
.
![Page 3: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/3.jpg)
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.
![Page 4: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/4.jpg)
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
![Page 5: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/5.jpg)
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.
![Page 6: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/6.jpg)
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
![Page 7: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/7.jpg)
(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
![Page 8: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/8.jpg)
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 )
![Page 9: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/9.jpg)
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:
![Page 10: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/10.jpg)
![Page 11: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/11.jpg)
![Page 12: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/12.jpg)
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
![Page 13: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/13.jpg)
Q11. Derive Schrodinger Equation for a particle in a one dimensional "box" and find its energy (eigen ) values, wave (eigen) functions and probability.
![Page 14: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/14.jpg)
![Page 15: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/15.jpg)
![Page 16: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/16.jpg)
![Page 17: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/17.jpg)
Q.12 Explain the formation of energy bands in solids
![Page 18: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/18.jpg)
![Page 19: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/19.jpg)
Q.13 Distingush between insulator, conductor, and semiconductor.
1. Conductors
![Page 20: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/20.jpg)
2. Semiconductors
3. Insulator
![Page 21: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/21.jpg)
Q. 14 Explain in detail the comparison among Maxwell Boltzmen (M-B), Fermi Dirac (F-D) and Bose-Einstein (B-E) statistics
![Page 22: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/22.jpg)
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
![Page 23: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/23.jpg)
![Page 24: Modern Physics - WordPress.com · 2016. 10. 20. · Modern Physics Q1. What is matter wave? Or What is Debroglie hypothesis? Ans: 1. According to debroglie hypothesis, any moving](https://reader036.vdocument.in/reader036/viewer/2022071606/6142f6f97bbb8b33111727bc/html5/thumbnails/24.jpg)
The-end