find the wavelength of hydrogen spectral lines (balmer series)

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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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.

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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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find the wavelength of hydrogen spectral lines (balmer series)

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