No. of Printed Pages : 8

PHE-11

BACHELOR OF SCIENCE (B.Sc.) LO LC) w—i

Term-End Examination December, 2011 PHE-11 : MODERN PHYSICS

O

Time : 2 hours

Maximum Marks : 50

Note : Attempt all questions. The marks for each question are indicated against it. You may use calculator and log tables. The values of the physical constants are given at the end. Symbols have their usual meanings. 1. Attempt any five parts : (a)

2x5=10

Calculate the deBroglie wavelength of a 10 eV electron.

(b)

Why is the variation of mass with velocity not apparent in our daily observations ?

(c)

State the selection rules for atomic transitions that yield characteristic X-ray spectrum.

(d)

Explain the function of a moderator in a nuclea‘r reactor.

(e)

Write the electronic configuration of Rubidium (Z=37).

(f)

Explain the use of radio isotopes for crop mutations.

(g)

Why can a particle in a box not have zero energy quantum mechanically ?

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2. Attempt any two parts : (a)

5x2=10

The area of a square as measured from the frame attached to it is A0. What will its area be with respect to an observer moving with relativistic velocity V along one of the sides of a square ?

(b)

Prove that under Lorentz transformation, /2 )] is invariant. the quantity [P 2 1 E2

(c)

A free neutron at rest has a mean life time of 900s. Determine its mean life time measured by an observer moving relative to the neutron at a speed of 0.8 c. If the observer moved with the neutron, what mean life time would he/she measure ? 4+1=5

3. Attempt any two parts : (a)

5x2=10

Show that Hermitian operators have real eigen values.

(b)

Show that the wave function tir(x, t)= A cos(kx — wt) does not satisfy time-dependent Schrodinger equation but satisfies timeindependent Schrodinger equation for a free particle.

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(c) A particle is described by a wave function 2Trnx — sin

for 0 < x <1= 0

elsewhere. Determine the expectation value of the momentum of the particle.

5x2=10 4. Attempt any two parts : (a) The wave function of a particle of mass m inside an infinite square well of width 37x + Bsin 31Tx a(— —a to a )is 41(x) = Acos a 2— a 2 Obtain the values of A and B and the eigen energy corresponding to the above eigen (b)

function. Using the uncertainty principle, show that the dimension of the most stable state of hydrogen atom is of the order of first Bohr

(c)

radius (a0). Using Hund's rules, determine the ground state term of Si.

5x2=10 5. Attempt any two parts : (a) Calculate the half-life of a radioactive 1 16 th of its substance, if its activity drops to — initial value in 40 years.

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(b)

Describe a model used for explaining the properties of nuclei, which are spherical or nearly spherical in shape.

(c)

Draw the schematic diagram of a cyclotron and explain its working. Is it suitable for accelerating electrons ? Explain.

Physical Constants : h =-- 6.626 x10 -34 Js me = 9.1 x 10 - 31 kg m =1 6725 x 10 27 kg P m n =1.6747 x10 -27 kg

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1. 1. : (a)

el

') 10 eVT--qtrff .

.fftrik0

I (b)

A-TT T1T2T fa--4-{7 tgft 1>311-11* 31 4 ,aturt 4911 4-1u1 go' fq9.4 31-N7raTi-crrw x-f-*-Tur 3171 6101 t I t-1 4-111(4. .

(c)

(d) (e)

.9T5.1-47 ft7"qa7 fq11.-qW T 4)14 s414-1 (Z=37)

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(f)

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(mutations) 14 W371431-174acf

t -1 4-1*.141 31-17:17, fT-4-d

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5

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5x2=10

2. cb 9417 : (a)

i&ch 4-179 3qk Trrn .a.7 179'

Ao 1114i 'A• .t) T art7

31-rcI-Tw1-4 r j; -4 -cm t dict)1

(b)

(c)

f

TTC7T

ch

[p2 (E2/2

t dt i

fqTFITqT2TT 14 #2.1.T

11 771

A`lchichlo 900 s tI -Pot t 0.8 c

ATE

.) TINT TITTEftT 3-t14-d

tf -cm #

71-q-9. oral .1,41 ? 3

7TRT

(*do wrr

4+1=5

laTff 4-11+11?

3. ch iqh.irTr : (a)



tUT1fi Tr-4-a- 4.1.)Rcb't 37117

5x2=10 TIF cmci gal

~ld tI (b)

tt7T1 ft c1 , 14-)(1-1 : 45(x, t) = A cos(kx —wt)

WZ-47 WZ-47 PHE-11

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ohm TR VT! =mot t



(c) T:b WIT " -T It 141c1-1 1:1 4-11 irtSicl t :

IP

Trnx 2 , 0
cbui

*T 147 51TEI -0 I

4. We7hITTF : (a)

a(-

2 2

3-197 opt-i 14

5x2=10 #947

m alrl -crw Lnci t : 3Trx li(x) =A cos+B sin 3Trx

a a

AatBt -R9f9"-*-T- 33 d)4kt7773-17 410-1* k1+10 3749. d1 ,41 *T 1:19' fit( I (b)

3lfir797UT #1-41a. 3171'7 -kaTI alftl*P-IT* 3-1-d7R.TT*F 3-1-FITtf, (a0) 6lcit t I

(c)

V:r"*f.97114

ztrtrr arlmr

Trru 01 PHE-11



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5x2=10

5. ail %.ITTFO : (a)

t or) rs4Nrcle.ci *irsbicil 40

.

z:rk 1TH — tR:rr

16

-

(b)

4

cm • -1

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cr72i 31.4-39 1-1 tch rid -0 I

1&rn Hiso auk +I

ci.; 7

OMR ziT 77917

riicnk 7 TRP:6 ci Itsq r11 A-91

(c) ohl



-T-dT

t

3-ft'

ftff

TzrTr ZCFOr fwzir iT Omni ?

Or4 - W PitictIct) : h = 6.626 x 10 - 34 Js

me = 9.1 x 10 -31 kg mp = 1.6725 x 10 -27 kg ni p

=1.6747 x10 -27 kg

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