Indira Gandhi National Open University (IGNOU) 2005 B.Sc Physics Modern - Question Paper

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BACHELOR OF SCIENCE <B.Sc.)

Term-End Examination

December, 2005

PHE-X1

PHE-11 : MODERN PHYSICS

Time : 2 hours Maximum Marks : 50

Note : Attempt all questions, The marks for each question are indicated against it. The symbols have their. usual meanings. The ua/ues of the physical constants are giuen at the end. You may use log tables,

1. Answer any five parts : 5x2

(a) Explain how the twin paradox is resolved.

(b) A rocket is moving with a speed of 0 -8c with respect to the Earth in a certain direction* It is given an additional velocity 0*5c. What is its final velocity ?

(c) Explain why we do not observe the mantfestaiidns of wave particle duality in the macroscopic world.

(d) Show that for a particle moving in a circle, the ' uncertainty principle can be expressed as A L & Q ft, where L is the angular momentum and ft, the angular position of the particle.

{e) Draw the energy level diagram (upto n - 4) of a quantum oscillator executing simple harmonic motion.

(f) Obtain the spectral terms for the n = 2 state of a hydrogenic atom.

(g) State giving reasons if the following reactions are possible :

(i) p + p p -f A⁰ +

(ii) rC + p n + %

2. The Milky Way galaxy is about 10⁵ light years across. For protons having relativistic energy of the order of 1G²⁰ eV, calculate

(a) the energy of the protons in joules,

(b) the increase in their mass, and

(c) the time taken by a proton to cross the galaxy in its own frame. ,

Rest mass of the proton = 1-67 x 1CT²⁷ kg. 2+3+6

OR

(a) An event occurs at x = 10 km, y - 1 km,

z = 2 km and t = 5 s in the frame of reference S. What are the coordinates of this event in 5', moving relative to S along the xx'-axes at a speed 0*9c ? 5

(b) A galaxy emits light of frequency 1*2 x 1G¹⁵ Hz. It is measured to be 6 x 10¹⁴ Hz on the Earth, Calculate the speed of the galaxy with respect to the Earth, 5

3. Attempt any two parts : 2x5

(a) Show that the eigenvalues of a hermitian operator are real.

(b) The average kinetic energy of a free electron in a metal 5s I j at high temperatures. At what

temperature would the electrons average de-Broglie wavelength be 0-5 nm ?

2

(c) Normalise the wave function \y{x) = AeT^x ,

Explain the concept of spin angular momentum. Determine (cs, a] and [0, cj, given

'0	1)			f0	1
		1	a ~
	0;			J .	0;
'1	o¹
,0		h

and

(c) X-rays of wavelength 1-5 A are incident on a sodium

<b>

a *

chloride crystal with d-spacing 2'8 A. What is the highest order maximum that can be observed in the, diffraction pattern ?

5. Attempt any two parts : 2x5

(a) Calculate the fission rate for required to produce 500 MW of energy and the energy released in complete fission of 500 g of Energy released per fission of ²U is 200 MeV,

(b) Show that the radius of curvature of the path of a particle inside a cyclotron is proportional to VN , where N vs the number of times the particle is accelerated across the space between its dees.

(c) Explain the working of a nuclear reactor with the help of a schematic diagram.

Physical constants :

h = 6-626 x 10'³⁴ Js m_e = 91 x 10^-31 kg k = 1-38 x 10²³ J K"¹

6 02 x 10²³ mol^-1

N:

PHE-11 4

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