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8/19/2019 Find the wavelength of hydrogen spectral lines (Balmer Series)
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8/19/2019 Find the wavelength of hydrogen spectral lines (Balmer Series)
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CONTENTS
Page no.
Abstract 2 Introduction 2
• Bohr’s Atomic model 3
• Hydrogen spectrum 4
• Balmer series 5
Methods and materials
• Apparatus
!"perimental procedure
#esults $%
• &or #ed light $%
Percentage error $%
• &or 'ur(uoise light $$
Percentage error $$
• &or Blue light $$
Percentage error $2
• &or )oilet light $2
Percentage error $2
*iscussion $3• Balmer lamp $3
• Po+er supply ,or Balmer lamp $3
• -otes on operation $3
onclusion $4
/ources o, error $5
#e,erence $5
Appendi" $5
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ABSTRACT
'he purpose o, this e"periment is the study o, the 0isible
spectrum o, hydrogen atom by means o, Balmer lamp that
enables us to per,orm an important (uantitati0e comparison
bet+een theoretical and e"perimental results. 'he purpose o,
this e"periment is to 0eri,y the (uantum nature o, the Balmer
series1 speci,ically ,or atomic hydrogen1 using sodium as a
calibration source. 'he calibration o, a di,,raction grating
spectrometer using a source o, no+n +a0elength +as made.
'he calibrated spectrometer +as then used to determine the
+a0elengths o, lines in the spectra o, atomic hydrogen and
other atoms. 'his +as achie0ed by calibrating a transmission
di,,raction grating using a sodium spectral source1 +hose line
+a0elengths +ere +ell no+n. 'he spectral lines in atomic
hydrogen and helium +ere then measured and their
corresponding +a0elengths calculated using the data obtained
through the calibration. 'he e"perimental results yielded an
appro"imation o, the #ydberg constant1 #1 +as ,ound # $.%
" $%6
m$
.
INTRODUCTION
In this experiment we will use a diffraction
grating optical spectrometer to study atomic spectra. we
will use the calibrated spectrometer to observe and
measure the spectral lines of hydrogen
Background: The diffraction grating provides the simplest and
most accurate method for measuring wavelengths of light. Itconsists of a very large number of fine, equally spaced, parallel
slits, usually thousands of lines (slits) per centimeter.
Transmission gratings are ruled on glass and the unruled areas
transmit the incident light. This experiment uses a transmission-
grating replica.
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Diffraction refers to the "bending" of waves around sharp
edges or corners. The slits of a grating give rise to diffraction and
the diffracted light interferes so as to set up interference patterns.
Complete constructive interference occurs when the phase or path
difference is equal to some whole number of the wavelength. In
general the grating equation for constructive maxima is
+here m is called the order o, the spectrum1 7 is the
+a0elength1 d is the spacing bet+een grating lines1 and 8 is the
di,,raction angle measured +ith respect to the direction o, the
light incident on the grating.
9hen the light ,rom a gas discharge tube is obser0ed +ith a
spectrometer1 the colored images o, the entrance slit appear as
bright lines separated by dar regions: hence1 the name line or
discrete spectra. !ach gas emits a particular set o, spectral lines
and has its o+n characteristic spectrum. 'he discrete lines o, a
gi0en spectrum depend on the atomic structure o, the atoms and
are due to electron transitions. 'he line spectrum o, hydrogen +as
e"plained by Bohr;s theory that describes spectral lines asresulting ,rom electron transitions bet+een energy le0els.
'he Bohr model +as based on the ,ollo+ing assumptions.
• 'he electron in a hydrogen atom tra0els around the nucleus
in a circular orbit.
• 'he energy o, the electron in an orbit is proportional to its
distance ,rom the nucleus. 'he ,urther the electron is ,rom
the nucleus1 the more energy it has.
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•
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orbit thereby radiating the di,,erence in the energy o, the t+o
orbits. 'his energy gi0es rise to a particular line in the spectrum.
'he ,ormulation o, 0arious series in the Hydrogen
spectrum is sho+n by an energy le0el diagram. 'he energy
corresponding to nF$ is sho+n along the lo+ermost line.
'he ,re(uencies o, lines in di,,erent series remarably
coincide +ith the 0alues calculated ,rom Bohr’s ,ormula.
Ho+e0er1 be,ore that1 the line spectrum o, hydrogen +as
sho+n to ,ollo+ the description o, Balmer;s empirical ,ormula:
= R2−
2 = −
2
Here1 n re,ers to the principal (uantum number o, the
initial energy le0el1 and R is #ydberg;s constant +ith a 0alue o, R
= 1.097 x 107 m-1.
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BA>M!# /!#I!/:
Balmer series o, spectral lines is produced +hen F 2
G F 31 41 51..etc. by e(uation D"E
=1.09737×10−32−
2
A$
'his series lies in the 0isible Dor opticalE region. 'he
+a0elength o, the ,irst member o, Balmer series is:
First member:
In this case F 2 G F 3
=1.09737×10−3
2 − 2 A$
F 5.2J nmLimiting member:
'he +a0elength o, the limiting member can be calculated
by putting F
In this case F 2 G F
=1.09737×10−32−
2
A$
F34.5nm
In this e"periment1 the hydrogen line spectrum +ill be
obser0ed and the e"perimental measurements o, +a0elengths +ill
be compared to those predicted by Balmer;s e(uation.
'he +a0elengths o, the spectral lines obser0able +ith the
Balmer lamp are indicated as:
/r.K n >ine 9a0elengthDnmE olour
$ 3 HL 5.2J #ed
2 4 4J.$3 'ur(uoise
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3 5 434.%5 Blue
4 4$%.$6 0iolet
'o ,ind a particular +a0elength1 use the relation:
Fg/in
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9here β=tan− )
G g: rating constantF $.6 $% m$
D,or a di,,raction grating o, %% linesNmmE
i, care is taen to ensure that the light enters the grating
+ith normal incidence1 the +a0elength o, spectral line is gi0en by
the ,amiliar relation
9here d is the spacing o, the Oslits in the grating1 m is the
order o, the di,,racted +a0elength1 and is the angle throughƟ
+hich the +a0elength has been de0iated. A set o, Balmer lines
originating ,rom 0arious energy le0els is schematically sho+n in
,ig.
&ig: Balmer lines originating ,rom di,,erent energy le0els o,
Hydrogen atom.
A schematic arrangement ,or the ,irst three di,,raction
orders o, the Hydrogen spectrum is illustrated in the ,ig:
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&ig: /chematic diagram sho+ing ,irst three orders o, the hydrogen
spectrum.
METHODS AND MATERIALS
"##$r$t%s:
Balmer lamp
Po+er supply o, Balmer lamp
/mall optical bench
Bench clamp
Ad?ustable slit
Holder +ith spring clips
opy o, #o+land gratingD%% linesNmmE
'ranslucent screen
Multi clamps
>enses ,F$%%mm and ,F5%mm
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EXPERIMENTAL PROCEDURE
Mae ,ine ad?ustment ,ocus o, the Balmer lamp to the slit1
,ocus %th and $st inter,erence order on the translucent screen.
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&ig: hydrogen spectrum obtained ,rom the e"periment.
RESULTS
&IH'*istance o, red line ,rom right F $.J%cm
*istance o, red line ,rom le,t F $.65cm
A0erage distance F dr F . . F $.665cm
, 3 F spacing bet+een the con0ergent lens and translucent screen F 4.2cm
As1 F g/in
Here1 β=tan− )
/o1.
4.2−1
E F−1
%.42cmE F 22.6Jo
&rom F g/in
9here1 g F $.6 $% m$
= ($.6 $% m$)sin(22.6Jo)
= 6.46 $%6 m F 4.$nm
P!#!-'A! !##
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A0erage distance F dt F . . F $.4%cm
, 3 F spacing bet+een the con0ergent lens and translucent screen F 4.2cm
As1 F g/in
Here1 β=tan− )
/o1.
4.2−1
E F−1
%.33cmE F $J.2o
&rom F g/in
9here1 g F $.6 $% m$
= ($.6 $% m$)sin($J.2o) = 5.2326 $%6 m F 523.2nm
P!#!-'A! !##
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/o1.
4.2−1
E F−1
%.2cmE F $.$6o
&rom F g/in
9here1 g F $.6 $% m$
= ($.6 $% m$)sin($.$6o)
= 4.6507 $%6 m F 45.%6nm
P!#!-'A! !##
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= 4.2010 $%6 m F 42%.$%nm
P!#!-'A! !##M!# >AMP
'he Balmer lamp is an a.c. operated ,illed gas discharge
tube ,illed +ith +ater 0apors. 'he sealed tube is supplied by a
+ater bound in hygroscopic material. 'he +ater molecule are split
up by the electron discharge in atomic hydrogen and hydro"yl
group. A high temperature resistant capillary inside the lamp
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,orces the discharge into a narro+ space +here a high
concentration o, atomic hydrogen is responsible ,or intensi0e
Balmer spectrum.
P@ &
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disappear a,ter appro". $ hour’s operation. 'he o"ygen lines in
red and green spectral region +hich are 0ery +ea compared
to Balmer lines +ill remain.
CONCLUSION
'he results obtained ,rom the e"periment ga0e appro"imate
0alues o, +a0elengths o, the Hydrogen Balmer lines1 4.$nm1
523.2nm1 45.%6nm1 42%.$%nm. 'he no+n 0alues o, the
Hydrogen Balmer lines 5.2Jnm1 4J.$3nm1 434.%5nm1
4$%.$6nm respecti0ely. +hich ?ust ,alls +ithin the e"perimental
uncertainty gi0ing us an accurate result.
'he 0alues o, the +a0elengths o, the Hydrogen Balmer
lines +ere ,ound to be1
Balmer line Measured
value DnmE
'rue )alue
DnmE
Percentage
error
HL 4.$ 5.2J $.46
523.2 4J.$3 6.3
45.%6 434.%5 6.$4
42%.$% 4$%.$6 2.42
'hese 0alues ,all relati0ely close to the true 0alues although
they ,all outside o, the errors.
'he 0alues ,or the Hydrogen Balmer series also ga0e rise toan appro"imation o, the #ydberg constant1 # # F $.% " $%6 m$
'he actual 0alue o, # is gi0en as1 # F $.%6 " $% 6 m$ so the
e"perimental measurement +as an accurate appro"imation.
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SOURCES OF ERROR
• Instrument resolution
• &ailure to calibrate or chec =ero o, instrument
• &ailure to account ,or a ,actor
•!n0ironmental ,actors
• Instrument dri,t
REFERENCE
• 'he American Institute o, Physics Handboo D$2 th editionE
• Introduction to the /tructure o, Matter1 RR Brehm G 9R Mullin1
9iley Dinside co0erE
• 'he American Institute o, Physics Handboo D$2th editionE
• ourse Manual
• 9iipedia
APPENDIX
(r$ting )onst$nt:
In this ,ormula is the angle o, emergence Dcalled de0iation1 *1 ,or
the prismE at +hich a +a0elength +ill be bright1 d is the distance bet+een
slits Dnote that d F $ N - i, -1 called the gr$ting )onst$nt1 is the number o,
lines per unit lengthE and n is the Sorder numberS1 a positi0e integer Dn F $1 21
31 ...E ...
*i++r$)tion (r$ting:
*i,,raction grating is optical de0ice used to learn the di,,erent+a0elengths or colors contained in a beam o, light. 'he de0ice usually
consists o, thousands o, narro+1 closely spaced parallel slits Dor groo0esE. ,#e)tr%m:
'he spectrum is the group o, colors that a ray o, light can be
separated into including red1 orange1 yello+1 green1 blue1 indigo and 0iolet:
the colors can be seen in a rainbo+.
,lit:
A long narro+ cut or opening.
X___________________________________________________ M. Usman Mustafa Group 5 (Leader)
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