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V Semester B.Sc. Examination, Nov./Dec. 2013 (New Scheme) (Semester Scheme) (2013 -14 & Onwards) PHYSICS – VI Astrophysics, Solid State Physics and Semiconductor Physics Time : 3 Hours

Max. Marks : 70

Instruction : Answer 5 questions from Part – A, 5 questions from Part – B and 5 questions from Part – C. PART – A I. Answer any five of the following. Each question carries eight marks.

(5×8=40)

1) a) Define apparent magnitude and absolute magnitude of a star. Hence, obtain the distance modulus expression. b) Obtain an expression for core temperature of a star.

(4+4)

2) a) Obtain an expression for pressure gradient of a star. b) What are Black Holes and event horizon ? Write the expression for Schwarzschild’s radius.

(4+4)

3) a) What are Miller indices ? Explain the procedure of finding these Miller indices with an example. b) What is Fermi level ? Write the expression for density of electronic states per unit volume of the free electron gas (case of three dimensions) and explain the symbols. Show, graphically, the variation of density of states with energy of the electron. (4+4) 4) a) What is Compton effect ? Obtain an expression for Compton shift in wavelength. b) Write the expression for thermal conductivity of metals on the basis of free electron model and explain the symbols. (6+2)

P.T.O.

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5) a) What is superconductivity ? Define the terms critical temperature, critical field and critical current density. b) Distinguish between Type I and Type II superconductors.

(4+4)

6) a) Obtain an expression for hole concentration in an intrinsic semiconductor. b) Write the expressions for electron and hole concentrations in an extrinsic semiconductor. How does the temperature affect the charge carrier concentration ? (5+3) 7) a) What is transition or junction capacitance of a p – n junction diode ? Explain. b) Distinguish between p – n junction diode and Zener diode.

(4+4)

8) With a hybrid equivalent circuit of a CE transistor amplifier, obtain expressions for current gain, voltage gain, input impedance and output impedance.

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PART – B II. Answer any five of the following. Each question carries four marks.

(5×4=20)

1) Calculate the gravitational binding energy of the Barnard star of radius 2.38 × 108 m and mass 4.6 × 1029 kg. If the star were to shrink to half this size, calculate the thermal energy liberated. G = 6.67 × 10–11 N m2 kg–2. 2) Calculate the mass of a main sequence star that has a luminosity 50 times that of Sun. Mass of Sun = 2 × 1030 kg. 3) The star Sirius – A emits peak intensity at a wavelength of 304.2 nm. Calculate its luminosity. Given : Radius of Sirius – A = 1.32 × 109 m, Wien’s constant = 2.89 × 10–3 mK Stefan’s constant, σ = 5.68 × 10–8 Wm–2 K–4. 4) X – rays of wavelength 0 .71 A are reflected from the (110) plane of a rock


salt crystal of lattice constant a = 2 . 82 A . Calculate the corresponding glancing angle for second order reflection.


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5) A current of 50 A is established in a copper slab of thickness 0.5 cm and width 2 cm. The slab is placed in a magnetic field of 1.5 T. The magnetic field is perpendicular to the plane of the slab and to the current. The free electron concentration density in copper is 8.48 × 1028 electrons/m 3. Find the magnitude of Hall voltage developed across the width of the slab. Given : Charge on electron = 1.6 × 10–19 C. 6) A battery of emf 2V is applied across the block of a semiconductor of length 0.1 m and area of cross section 1 × 10–4 m2. If the block is of intrinsic silicon at 300 K, find the magnitude of total current. Given : For Silicon at 300 K, 2 −1 −1 electron mobility, μe = 0. 135 m V s 2 −1 −1 hole mobility, μh = 0 .048 m V s

intrinsic carrier concentration, ni = 1. 5 × 10 16 m −3 e = 1.6 × 10–19 C 7) A load resistance of 2 kΩ is connected in the collector branch of an amplifier circuit using a transistor in common-emitter mode. The current gain β = 150 . The input resistance of the transistor is 1 kΩ . If the input current is changed by 50 μA , (a) by what amount does the output voltage change and (b) what is the power gain ? 8) Calculate the current through the load resistance RL, voltage across RL, diode power and load power in the circuit shown below.

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PART – C III. Answer any five of the following. Each question carries two marks.

(5×2=10)

a) Why is the bolometric correction always negative for any star ? b) Compare the color of class ‘O’ star with that of class ‘M’ star justifying your answer. c) An external magnetic field applied on a superconducting material may destroy its superconductivity. Explain. d) Is Bloch theorem applicable to constant potential ? Justify. e) What is the probability of finding an electron at Fermi level at i) T = 0 K and ii) T > 0 K ? f) In what direction does the Fermi level move in a semiconductor doped with donor impurity as the temperature increases ? g) The ratio of number of electrons to holes in an intrinsic semiconductor at temperature T is x. What happens to this ratio when the temperature is increased to 2T ? Justify. h) Why are Si and Ge not used in the construction of LEDs ? ———————

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V Semester B.Sc. Examination, Nov./Dec. 2013 (OS) (Semester Scheme) (Prior to 2013-14) PHYSICS – VI Quantum Mechanics, Atomic and Molecular Physics Time : 3 Hours

Max. Marks : 60

Instruction : Answer five in Part – A, four in Part – B and five in Part – C. PART – A Answer any five questions. Each question carries six marks.

(5×6=30)

1. Explain how classical physics fails in explaining (a) photo electric effect (b) atomic spectra.

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2. a) Obtain an expression for de-Broglie wavelength and express it interms of energy and temperature. b) Discuss how de-Broglie’s concept explains the Bohr’s postulate.

(4+2)

3. State and verify Heisenberg’s uncertainty principle with the help of gamma-ray microscope experiment.

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4. a) What are operators in quantum mechanics ? Explain briefly the various operator representation for the dynamical variables. b) Discuss probability density and normalization.

(3+3)

5. Obtain energy eigen values and eigen function for a particle in a one-dimensional box of infinite height. 6. Give an account of Sommerfeld’s relativistic atom model.

6 6

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7. a) Explain the concept of space quantization. b) Obtain an expression for magnetic moment due to the orbital motion of the electron.

(3+3)

8. Give the experimental arrangement and quantum theory of Raman effect.

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PART – B Solve any four problems. Each problem carries five marks.

(4×5=20)

Make use of the data given below wherever necessary : Mass of electron (me) =

9.1 × 10–31 kg

Charge of electron (e) =

1.6 × 10–19 C

Velocity of light (c)

=

3 × 108 ms–1

Planck’s constant (h)

=

6.63 × 10–34 JS

9. Find phase velocity and group velocity of an electron whose de-Broglie wavelength is 1. 55 A .


10. Find the uncertainty in the frequency of radiation if the average period that elapses between the excitation of the atom and the time of its radiation is 10–8 s. 11. Calculate the zero point energy and the spacing of the energy levels in a onedimensional oscillator with period 0.714 ms. 12. If the mean wavelength of sodium D-lines is 589 nm estimate the minimum energy in electron volt of the bombarding electron for excitation of these lines.

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13. Calcium line of wavelength 423 nm exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4T. Calculate the frequencies of normal Zeeman pattern observed. 14. In the CO molecule the wave number difference between the successive absorption lines in the pure rotational spectrum is 384 m–1. Calculate the moment of inertia of the molecule and the equilibrium bond length of the molecule. Masses of the 12C

and 16O atoms are 1.99 × 10 –26 kg and 2.66 × 10–26 kg respectively. PART – C

Answer any five of the following. Each question carries two marks.

(5×2=10)

15. a) Is classical concepts valid in the region of atomic dimension ? Explain. b) Can matter waves travel faster than light ? Justify. c) What is the significance of the magnetic quantum number m ? d) How does the motion of the nucleus affect the wavelength of the spectral lines ? e) Why does normal Zeeman effect occur only in atom with an even number of electron ? f) Why do all molecules not show rotational spectra ? ———————