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Unformatted text preview: Ska/72w EXAM 2—April 9, 2010 Phy63 Spring 2010 v.A Name: Rec: Section AmMultipIe Choice (5 points each) 1) A proton has a rest massenergy of mp02 x 940 MeV (approximate), and a radius
of 1 fm (Fermi). In order to have a deBroglie wavelength the size of a typical
atom (~ 0.1 nm), what is its kinetic energy? .0082'ev , : ﬂ, 3: ﬁg yawn/d 5
x2 P0 to , S.
(b) 12,400 eV(12.4 keV) é’c VH6 mu (2 2
is g; :: _..—
(c) 0.164 eV 1
(d) 6,200 eV (6.2 keV) My: reﬂexes; : L (h: lanky/31.13.. (e)10.06eV ,2 MP 2 ﬂ}: 2) Using the uncertainty principle, estimate the level broadening (uncertainty in the
energy of the energy level) for an excited state of an atom, which has a lifetime of Ins:
. — A if
.O.33p.eV At 4i "’ 2 B
_ f 1/ ~ (b)0.44n1eV AE /_ L _.__ _./__ .1 C ” Zaﬁ' 2 27? Aft/1 V5;
(0) 0.55 eV __ /24’—0 e l/MM
(d) W ' 4;; (gem/mfg)
(e) lMeV # [2&0 #586 V (Ll) 3) A hydrogen atom is placed in a magnetic ﬁeld B, pointing in the +zdirection.
For an electron in an 1 = 1 orbital, what is the appropriate energy diagram? Note
that the magnetic interaction is given by E m  u . B, where p, is the total magnetic
moment, including the orbital and spin contributions. (a)  3 '. .
' (b). (a ’ (e) ' 4) In the decay process 2125;sz 9 21233Bi + , what is missing on the RHS (right
handside)? 6' + v [mswve (ﬁre/age l/ 8 (6.) 5325:83c3'ffe) V13 (50
(b) 6'" + i? K ,
(c) e Mfffrﬂ 089W WLLM6“W (d) e+ + v (e) e" + v 5) A certain specimen is prepared as a mixture of 2 radioactive elements X and Y.
The ratio in number of atoms is 2:1 (X2Y). Each type of atom is transmuted into
atoms other than X or Y. In other words, after each decay, the number of X or Y
is decreased by one, respectively. The half life of X is 7000 yrs, and for Y it is
700 yrs. After a time t, it is found that the ratio has become 16:1. What is time t? *fﬁz
(a) 700 yrs N)“: MXO 6 ”MW"; V 8 (’15)
612
(b)1560yrs Afr: Me €”%ﬁjg MC (14)
(c) 1333 yrs A/ ﬁgézﬁzﬁwh 752%]
(d) 3333 ’ All : M “H: ”i0 a
yI'S NY A}??? J—.
, «55$? [?0¢993vo]
.2333 yrs : 2 e ?
fnghwt I
62: (Z {n 7
£1, at: 3&2 :f42[?dmim]
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5 Section B——Truth/Fa1se (3 points each) 1) Emission of a single photon from the ZS to 18 level in hydrogen is an allowed dipole
radiative transition. T @
ﬂI/waaf PIIéo/e ﬁcmaBCr‘m A Z: i / 2) To make a laser operate, population inversion must be achieved. @ F 3) In nuclear ﬁssion of 235U, each ﬁssion reaction produces on average 2.5 thermal
neutrons directly in the decay process, which can lead to a chain reaction. T (19 @0444? neg/Mags are lb/ncltece/ czf/ew ﬁeﬁsf’ﬁwﬁ WWW;
Q/rQ S‘IZWEJ fly {$52 prawne ryﬁamﬁ/ﬂﬁm, 4) Stable heavy nuclei with larger atomic number Z tend to have excess neutrons in
comparison to protons to help bind the nucleons together. (13 F 5) For a positronium, an “atom” made of a positron e+ and an electron e—, the lowest
quantum orbit (neglecting relativistic effects), is given by the Bohr radius, a0 =
(ll/21c)2/[kemc e2], where m6 is the electron (positron) mass. T (9
mg ta 249 A: rzﬁﬁce/f 5;; ”3? ”face “WM” :4“: v.8 7" MC 7*
F
7”
.. F
7° Section C—Long problems. Please show all work and justify your solutions/answers.
(20 points each). 1) For the harmonic oscillator in 1dirnension, the Schrodinger equation is:
(p2/2m + l/2rno)2x )X‘P mEﬂ’n, where the momentum operator is p =(\hbar/i)d/dx. The
normalized ground state wavefunction is given by LPo i Boexp[—ax2/2]. Note that _ +03 2 2 1/2 . 3 W
3—0;: Exp[ax ]dx (at/a) . 62  if
(a) If the second excited state wavefunction has the form: ‘Fz = B2(1 — sz)exp[ax2/2], determine the constant C based on the requirement
that: . +133
3 T2* T0 dx = 0 , i.e. the ground state and 2"‘1 excited state co
waveﬁmctions are orthogonal. Also, determine 130, but do not determine B2 (8 + 2
points) [Hintwuse integration by parts. ] ‘ 0" Q32 7% 2 I 7'
59 f ﬂ/Wncedga%m. f3): 4 abc 2/: 602 we ”DC :[gfj Be “ﬁ/BUSéé) 7 2. max”
C3 :E’gt4lZ30428221Lm [/“CZ 6 #6:; 2. 606 am .1
—I‘2 .06 2,4152 C ‘  ”a z... ’jea A”,
:3 ﬁﬁcécf :6 99625229 ﬁ‘gzsz’” ”(M)m’z€ $22—$47
m
$ :53 W /C=26L. (9
2 (b) Compute <x> and <(AX)2 > : <x2>  <x> for the ground state (1 + 3 points).
, or) , n {M .2
<1): £6qu c/«a/x ref” Xe—de {fog (A? awash?)
<@X)2> :' 05%»??? 05> #554 from ﬂea/L4 (ea) (2(2):???) [177/251, ._ (c) Compute <p> and <(Ap)2 >= <p2 > <p>2 for the ground state (2 + 4 points):
z
sax <p>: I: of fiﬁggmxﬁ’gw 1/77/4921); we ﬁg; twee)
<z¢i> : «61> " <79“ '3 “52>
”7770037?ng 4’" 9/ 41:35me “3‘3: ,tg/fa (LIV/5772i: it
emigﬂmMJi/ﬂy 7 MM“.
2&3 {we W m ’7 ﬁiﬁﬁ 2. 2) An atom with atomic number Z = 100 is stripped of all electrons except of one last
deepcore e". (a) What is the radius rn for principal quantum number n (3 points)? (c) Next, the K (n=1) and L (n=2) shells are ﬁlled with electrons, and one more
electron is added What is the energy of the lowest energy level that the extra
electron can occupy, and what 18 its radius (4 + 4 points)? X” 55226 BB: 2 efae’m . 2.323212? 2312M: 5%c/aéwg. 3% awe Wﬁéﬁzy C3 f5: a):
I}: «do . 2:5‘zf'y/am
(d) 4 more electrons are now added What is the lowest energy electronic
conﬁguration (4 points)? Weéaﬁ‘ 2 1». (P _;_ Z 7137;: /§‘ /92 2322p¢3523£
Mt [aytchaﬁs’ «Ma 3) Polonium 21234P0 undergoes adecay to Pb. (a) at is the disi ' of the decay process (5 points)?
' 2 x 2 . 203 9L
——2
We) lﬂfyM: Cd :: (121/.953695’58  45002503 ”20;. 9715535)“ X 95/ 494%? W W (b) What is the available kinetic of the a—partiele (10 points)?
[’0 21.96am @3473; ( Macias):
2‘ —
"if mﬂc Viki 1" {MFA Vi?) ‘" Egg? Hey ” ~ h .— _, ”Maggi/e
(“mg/M Mme“m' ”Ma: ”fieﬂuﬂ ”hr Rama? '— 0 r> 3“” 13/9" '5;
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ﬂ_> : Magi/{1k +5 (”3% 7:13;? : Engage [ff %]1&?J?ﬂ€y
_ — i 7": 1%., , :(SMoHeL/Z
khfﬂg‘m%%% %%*%%x§%ﬁﬂﬁ¢/ (0) Assuming that barrier to be a square barrier, what is the transmission probability
if the barrier height is 30 MeV, and the width is 10 fm (5 points) ? ,2cL (7 jgzggiiigiﬁZ%V
#, ; _*ﬂ_ﬁwrlﬂ,da /'::6 77
.— ‘ [S— ‘
, ; 2'@/g%X‘f0/% (249/5004)
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, , wa' WWM#WMﬁHi: “if j;
:5 ﬁgxixFxm/ 1 V, 3 ' 2‘9 .2 6 C.
: [if—f/Y'mmf Chemical and Nuc_le'ar_ Informatum for Selected Isotopes .3 ' .12992835;
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 Spring '10
 Chang
 Physics

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