TheNature of the Atom
.
Problem I
Irr the line spectrumof atomichydrogenthereis alsoa groupof lines known asthe Pfund
series. Theselines areproducedwhen electrons,excitedto high energylevels,make
transitionsto the n : 5 level. Determine(a) the longestwavelengthsand (b) the shortest
wavelenethsin this series.
t ,)dtuP4r-.4
V
A(+
/x=
f,N
q)
-Oz'gt*
'^^'W"j
^r"r". ^a ,W6roYL
bI
*)
',
rr=Lr?r8t""
)^r,^rat tytl\ rwcu/w uA]"r\ n = 6 @'^^'\)W tt)-'fu^)'
o?ru4i'nq/n
(n=u)
'/r=A(t^-+^)
(i^-lr')
YX-- (t.or1" lon'-')
= l'3't* lD5m-l
\ = r.qa ^ tD-bm
l,.=A(+ *)
lo"'-') (!r^-o) = 4'z1"lo'.-'
yr, - ( t.D1?*
^
-
)")'8"
lb-6n'
Problem2
(a) The elechonin a hydrogenatomis in the first excitedstate,whentle electron
acquiresah additionat2.86 eV ofenergy. What is the quantumnumbern of the stateinto
which the electronmoves?
V'
fr,
oru^ryy Afu'b4 at ftr )/"f;,QXu\."J''r
\yv.
h-n
---+Eo= - l?' G'v/^"
n - I
'+'t E=
nur -ont'tft,A
&
z.>
tVS=Y
'
A gv''-'t -UJ
tt
-3"'i.V
+ A.EGeV = -D.54e-V
- 15.Ice v
---.-
":F@
rE
f)t
r \ - \-
'= - 3.4.t1
- o. Sl e\)
r
(b) A laseris usedin eyesurgeryto weld a detachedretinabackinto place.The
wavelengthofthe laserbeamis 514 nm, andthe power is 1.5 W. During surgery,the
laserbeamis tumed on for 0.050s. During this time, how manyphotonsareemittedby
the laser?
P: t/"
X = 5l'l nm
'. fu -e/fzqt r/*'i'"
'{V
)e .l-an i'" q*-
P= 1"5w
t=nhT
9'+
9a
\.
6 = 9,o5D9
<l
n=?
., \4
Y= _";',
r
n= Ij-
ht
?=/^=
= (t"sw) Co,o5ot)
o'' fta)
(c,t z' I u'ltr.r) ( r.g"/*t
3.o , lD''f s
g t{ x lo-qr.,
= 5.8't x lo'ttfz
D:1,9*lo'"