This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Short Answer Questions: 1. Why does the existence of line spectra Violate classical physics? (4 pts.) , r (a) Write it and deﬁne all terms. (3 pts.) (0) Suppose you were scattering electrOns off a crystal. Coherent scattering requires the lattice
constant (spacing) to be of the same magnitude as the wavelength. Show how the wavelength
varies with the kinetic energy of a scattering particle. (4 pts.) ((1) Suppose a proton beam and an electron beam had the same energies such that 9L3 : 1 A. What ‘
would the wavelength of RP be? (Inp : 1836 me) (4 pts.) J6 ﬂ ma _.___ [lg/{1% 41, _/m r‘  4——
Ep‘ EB (ﬁrle *' (8% Ea 3. Postulate 111 (my pestulates) states ‘P(X) and 9100/62: must be everywhere... (3 pts. each) (a) continuous: what does that mean? 7% (b) s'ngle valued: what does that mean? . x ‘
M flu ‘ 5L M “a” a“ 4W WWWQW 4. Consider a particle in the box with conditions V = 0, 0 <‘X < a and V = 00 elsewhere. In the box the
Schrodinger equation can be written 62 2 '
Esra) =2—wa) (a) One possible set of solutions to this problem are the free particlesolutions
‘ﬂ : Aeﬁpxm and 1P" = Ae’jpx’” Show ‘l’+ is a solution to the Schrodinger equation. (3 pts.) agfwwxﬂw /r (b) Does ‘l’+ obey the ﬁnite conditions ofPostulate III for a {seal particle? Why or why not? (4
pts.) _ i . E K/ﬁ
l6 n (PX  f .. "Z
r. as. *(ﬁe we — a low
Weﬁxlgogbé (c) On a physical basis why are ‘P+ and ‘P_ unlikely solutions to the particle in the box? (4 pts.) ’ _
kl,qu MwWWrLlﬂM‘Lxmﬁw
1, p I , 30 WW ((4 pm [iiiLoam
W Li; Mummy 3:) W is —W “W
M (d) In cﬁs veal/Elena thi Lg t9 £24m cm,
below. (4 pts.) S \Piﬂioiﬁ'l’qji): ilemrna by taking linear combinations of T+ and ‘1’“. Determine these
J5 5K —T:KI‘ LIA
{3 n+6 {my WW% J§
E
if:
= §r=
X
h
D
:9
H
Yd
q> 4/:me ‘9‘ 0 (g) What are the conditions on ~2— such that ‘1’; obeys Poiétulate III? (4 pts.) Sketches for We and in are givexbelow ‘ ' ‘P \o/l classical—turning points _ I _ 'classicaltuming points (a) When v = 0 the wave function has the form given'ab‘ove. Carefully draw {’02 and ‘1112 below.
(4 pts.) 'y ..... / y classical turning points '  classical tuming points —A : AI/LX (b) Is Axo > 0 for v = 0? Why or why not? (Hint: you don’t have calculate it just use arguments
based on results above.) (3 pts.) 7 ' '\ A O ‘ , M  r @cégiﬂa I Wm km) (c) What value" of Ape corresponds to Axo? (Hint: X and p do not commute for the Harmonic Oscillator.) (4 pts.) H p D AXAQZ’a/L Xitﬁl‘TMW ((1) At the classical turning point (V(y) = E), To is not zero. Write an expression that would allow you to calculate the probability that the particle exists in the forbidden zone (i.e., where V(y) > E) ' f =. .
orv 0(40123ts) 41:08 ea 4‘01
30‘, éébpﬂaoo (i) the most time? :— O '
W, (Lil a M All, plagcéwocco (ii) the least time? %
W (P503) (#005?) *jj O [W ' Give a brief justiﬁcation for you answers. (f) For a classical Harmonic oscillator, like the pendulum, where does the oscillator spend... (4
pts.) ' (i) themosttime?  1,: _ _ W) W 32$”m_ W W Give a brief justiﬁcation for your answers. (g) State the correspondence principle. (3 pts.)  i " I _‘
/ . (h) What must happen to ‘Pvz as v gets large? (3 pts.) ' EU: (KOM2, (A190 L; wheat—eve / Eﬂaoo waQ " CJ . O “>5
H O l 00 Lil/O, glib. W
(i) Determine the average value of y for ‘Pv(y). (Hint: rec l the properties of even and odd
functions.) (4 pts.) ' (1') Determine the most probable values of y for v = 0 and V = 1.. (6 pts.) WW “NP; :0 (h) The classical turning point is given by ytp: at: (2V + 1)”? Are your answers in part 0)
consistent with the correspondence principle? Why or why not? (4 pts.) “at? [1710) 3 ( ...
View
Full
Document
 Winter '08
 BOWERS
 Physical chemistry, pH

Click to edit the document details