PHE-11
BACHELOR OF SCIENCE (B.Sc.) Term-End Examination December, 2009 00
O
PHE-11 : MODERN PHYSICS Maximum Marks : 50
Time : 2 hours
Note : Attempt all questions.The marks for each question are indicated against it. Symbols have their usual meanings. You may use log-tables or calculators. The values of the physical constants have been given at the end. 1.
2x5=10 Answer any five parts : A free neutron at rest has a mean life time of 900s. If an observer measures its mean life time as 3600 s, calculate its speed relative to the observer. The de Broglie wavelength of an electron is 5890 A. Calculate its kinetic energy in J. A microscope is used to locate an electron in an atom within a distance of 0.2 A. Calculate the uncertainty in the velocity of the electron. Give the electronic configuration for an atom having Z =19. (e) Explain with reasons whether the following reaction is possible or not : n —> p + +e– +ye
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Under what condition is the product AB of two Hermitian operators A and B, Hermitian ? The half-life of a radioactive element is 13.86 days. How much time will it take for 116th part of the material to survive ? 2.
5x2=10 Answer any two parts : The density of a substance in the rest frame S is 19.3 g cm -3 . Calculate its density in a frame moving with a speed 0.9 c relative to S. A spaceship moving away from the earth at a speed of 0.8 c releases a probe parallel to its direction of motion at a speed of 0.6 c relative to the ship. Calculate the speed of the probe relative to the earth. (c) The rest mass of a free proton is 938 MeV/c 2 . Calculate the relativistic mass, momentum and speed of a proton having kinetic energy 100 MeV. Take 1 MeV =1.6 x 10 -13j.
3.
5x2=10 Answer any two parts : (a) Which of the following wave functions are physically acceptable ? 4 (x)=- A sin kx e — x2 (x) = A e - x2 / (x - a), where A is a constant and - o < x < Explain giving reasons.
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The wavefunction of a particle in a 1-D at infinite square well of width 2a (- a to a) is = N COS(
given by 'I'
37rx 2a
Determine the normalization constant N. Establish the commutator [Lx , Ly ]= ihLz 5x2=10 4. Answer any two parts : (a) Calculate the expectation value of the kinetic energy for the ground state harmonic oscillator whose wave function is :
To (x) -
Where a2-
a \Y2
,Frr
_a2 x2
exp
2
mw
Calculate the normalization constant A for the wave function of the hydrogen atom in the second excited state, where the wave function is, 'I' (r,0,0) = A r e-r /2ao COS 0 •
Calculate the minimum voltage required for an X-ray tube with a 26 Fe anode to emit a Ka line. (Take cr= 2). Calculate the Frequency of the L to K transition if cr=10 in the L - shell. PHE-11
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5.
Answer any two parts :
2x5=10
How is energy released in a controlled manner in a nuclear reactor ? What is the imporance of the blanket in a nuclear reactor ? Obtain the expression for the distance of closest approach for an alpha particle incident on an atomic nucleus of charge Ze. Calculate its value for 4 MeV alpha particles incident upon gold nuclei (Z = 79). (c) Explain the principle and working of a cyclotron. How does a synchrocyclotron differ from a cyclotron ? Values of Physical constants : h = 6.63 x 10 -34 Js h = 1.05 x 10 -34 Js me =
9.1 X 10 - 31 kg
Mp 1.67 x 10 -27 kg 1 = 9 x 109 Nm2C-2
47 E0 c =3
x 10 ms -1 -o0o-
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cbik u l Trro t Trr :
k1 4-1 q1IfT F-1 4-11C1R5d 31fif-wzI1-4114
n --> p + +e — F e
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*- T \TIME
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(c)
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3.
(a)
5x2=10
:
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i
t
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— a),
—
1I L
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(x)= A sin kx e x2 (x) A e- x2 /
s.)-
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6
< X < co
fit -A
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fl - 1 -1
T (x) = Ncos(31Tx 2a ) •
N cb1
TIzeceT [Lx , Ly ]= ihLz q't
4.
1-71
ftr4
I 5x2=10
:
(a) airdt t-d-W
+10,TI dl\TI 1
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Y2 (1 To (x)= (-exp
—a2 x2 2
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1 1
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t
otA(51
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(a)
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grq
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:
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5.
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i
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t? PHE-11
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c 4 tH1 uja14
3114q1 Ze
ITT 3119fTd
F-1 ch dc1 1-1 3 .4 I I-11
c
I
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4 MeV 3-1T1F1
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=4-> i ct> Lk.)
#14t *111 -911-411
c1.C1)
.) •-licrcil,4-1 A t-A
^ldlt? 9 :
tr-d-w
h= 6.63 x 10 —34 Js
h =1.05 x 10 —34 Js e 9 1 >< 1 0 31 kg Mp =1.67 x 10 —27 kg 1 — 9 X 10 9 NM2C-2 41re. c =3 x 108 ms —1
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