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Unformatted text preview: NAME A N w t3: 59:1: ID#
EXAM III : Physics 213 Chapters 5 & 6 April 16th 2007 The exam contains FIVE questions on EIGHT pages. You must
show all work and give explanations. ****THE CORRECT ANSWER WITH NO EXPLANATIONS OR
WORK SHOWN IS WORTH ZERO POINTS. Conversely, the WRONG answer with all work shown will be given partial
credit IF the steps shown are logical. All answers reguire units and all vectors require direction.
All formulae are on a separate sheet. Good luck! Question 1. /20 points
Question 2. /20 points
Question 3 /40 points
Question 4 /30 points
Question 5 /40 points
TOTAL / 150
Useful constants 0:3 X l08m/s
Elementary charge, e=l .6 X 10"9 C Mass of an electron =9.l l, X 10‘31 Kg Boltzmann Constant k=l.38 X 10‘23J/K=8.62 X 10“5 eV/K
Stefan Boltzmann Constant 025.67 X 10’8 W/(m2K4)
80:8.85 X 10“2 F/m
l eV=l.6 X 10‘19 Joules
“0:431: X 10'7 T.m/A
Mass of hydrogen atom=l.6727 X 10'27 Kg
h=6,626 X 10‘34J—S=4.l36 X 10‘15 6V S jg
T, =h/21t =1.054 x 1034 J s =6ésax+eim casszx \o"”‘ 6V3 NAME Q. 1. The ﬁgure shows the wave packet for an electron. The momentum of this
particular electron is p=10'23 Kg m/sec. What are the uncertainties in Re‘lJ 0
e—‘ A ~>t
(i) (3 pts)Position (ii) ( 6 pts) Momentum m 3 [if
> My”? ) / (A W” ‘7:;:,_ a / ;
(iii) ( 8 pts) Energy __ Are these minimum or maximum values of the uncertainty? ( 3 pts)
é it f?
a é l/l/l‘" “AAA/V W NAME (2.2. ( 20 pts) An unstable particle called the eta meson has a rest mass of 549 MeV/c2
and a mean lifetime of 7.00 X 10"19 secs. What is the uncertainty in its rest mass? m 5% la: 6:3" V/Q, Uncertainty: NAME Q.3. A nucleon in a nucleus may be considered as a particle in a box where the dimensions of the box corresponding to the diameter of the nucleus i.e 10*14 meters. Take
the mass of the nucleon to be 10'27 Kg. (a) (12 pts) Draw the wave functions corresponding to the ground state, 2"d excited state
and 41h excited state (i.e. n=l,3 and 5 respectively). The wave functions should be drawn
to scale such that the relative periods, phases and amplitudes are clearly seen. Give
numerical values for the period in each case. 4‘“ excited state Ground state 2‘1d excited state (b)( 6 pts) For each of the above states, write the position(s) of highest probability of finding the nuclﬁeon.’g LI / L [j a; x: f f) _ r A;
( ../t}“eA./w£b fig " ' " ,_ . i' “A
W: I 'i I if
A {it/5 t W “a i it?
w. (c)( 7 pts) A nucleon makes a transition between the first excited state and the ground
state. Calculate the characteristic frequency of the transition. L I» H A i E, L. if if“: X
i; x t”? L1,; ti; 3 ‘ a * / {is}
if
\t
A
\J
{‘x
x Frequency f: * L d (d)( 8 pts)lf the nucleons were instead confined to an atomic radius i.e. 10“0 m how
would the characteristic frequencies change? Give both qualitative and quantitative answers. 1 ,_ , . ’i VVK,AAW5/lrk/ talij‘mﬂsl ths/xuéﬁt/m X L t w it“ Q” i, ,1 “I
viva“) t/mmu/x/éulaw n ' » lay a,” (e)( 7 pts) If instead electrons (mass=9.l l X 10‘31 kg i.e.~lO’30 kg) were confined to the
nucleus how would the frequencies of the characteristic energy level spectra change? ? Give both qualitative and quantitative answers.
is NAME Q.4. A particle of mass 10“30 Kg with energy 10‘20 J strikes a potential barrier of height ] l X 1020.] and width 1.0 nm. 100 million particles are incident on the barrier
coming from the left (a) (10 ptS)Sketch the barrier, indicating the relevant dimensions, as well as the energy of
the particle. a c a g a ,
‘C “if, “if; r?
91 i Number of transmitted particles: Zita!“
ﬂat
{2‘ f ,‘M§(c)( lO pts)The following changes are made on the barrier:
” 1. Increase mass of the particle by factor of 10
11. Increase the width of the barrier by a factor of 10
III. Decrease the energy of the incident particle by a factor of l0
Which single change will result in the greatest decrease in the transmission of particles? Write them in order of decreasing impact i.e. first list the change having the largest
impact finishing with the change having the smallest impact. If two or more are
equivalent indicate with an equal swig/gig / w.» XWWWW ‘ if; (i: ) NAME (2.5. The potential energy curve for a particular spring with spring constant k is shown.
A mass of 10‘27 grams is attached to the spring and the ground state energy for this spring/mass combination is 20X 10‘20 J . 100 CO
0 O)
O ENERGY (x 102° J)
3 M
O —10 5 (a)( 15 pts)What are the energies of the 15‘, 2"", 3rd excited states? * ‘ XL ,, x / ‘ l at 0%} a: A L _, éx 3:147 Zw r) N m ,5, Wet m a; M t Y: W l l/yy l“, EA.) 5;) {I (j) 4 {it 5;) 34L .2 we
LN l b l c m , ~ I‘ s5 “9; it pd} is; it; i ° i €i _ . if 5.. g x
{w / {7 Va, «J 0
/ r» a ’ 31/3 l ,2. ( lit} I 10 )3”, (.7) 2nd excited state: ,r * f3 ’ .3 “3%” 1/ / \ <3 <3; t 3rd excited state: i ﬂ if} R) l U 0 {O i; 4;} ‘ ¢ 35: ,, {M
a (b)( 10 pts)On the graph, mark the classical turning points of the ground state and first excited state. ix ’ / “a “‘ (:3 ,l
‘3 15‘ excited state: (’9 O k M} NAME (c)( .15 pts)lf instead the mass was 10‘“ Kg, what would the energy of the ground state
and subsequent excited states be? ...
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 Spring '07
 Adenwalla

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