laboratoryreport_spectralline_nguyendang_e1500966

Information Technology Degree Program

Principal of Modern Physic Laboratory Exercises

Lab No 4 – Spectral Line

Laboratory performed on

25/11/2015

Nguyen Hai Dang

Partner: Nguyen Tuan Minh, Nguyen Cong Danh

Team: 4

Class: I-IT-1N2

Date: 13/12/2015

_____________________________________

SPECTRAL LINE Nguyen Hai Dang 2 | P a g e

CONTENTS

ABSTRACT……………………………………………………………………….3

I. INTRODUCTION ............................................................................................ 4

II. EXPERIMENT PROCEDURE ........................................................................ 6

III. EXPERIMENTAL RESULTS ......................................................................... 8

IV. ANALYSIS ...................................................................................................... 9

Error calculation ............................................................................................... 9

Compare experimental result with literature value ........................................ 11

V. DISCUSSION ................................................................................................. 12

VI. CONCLUSION .............................................................................................. 16

VII. REFERENCES .............................................................................................. 16

VIII. APPENDICES .............................................................................................. 17


Abstract

The experiment was carried out with an aim to accurately analyze light emitted by an

atom by the use of diffraction grating, particularly transmission grating, in which

interference and diffraction are the dominant phenomena. Known spectral light’s

property of Cadmium was utilized to help arrive at the initially unknown distance

between two consecutive slits, d, which is (1.70 ± 0.05) µm. The groove density of the

grating had been found 588 slits/1mm, which is 2% smaller than the value from the

manufacturer. Consequently, known slit spacing was used to investigate spectral light’s

property of mercury. However, the resolving power of the grating in this experiment

had not allow for the observation of mercury’s first two wavelengths in their first order

fringes. The experiment can be improved by the implementation of grating of higher

slit density.


I. INTRODUCTION

Every atom emits and absorbs light of discrete frequencies, for the energy-level

diagram of each atomic element is unique to that element. For that reason, atoms of

certain element have their own unique finger print, which is their discrete spectral line

consisting of perfectly pure colors. Several methods has been devised to analyze

spectral line such as prism or grating systems. In this experiment, spectral line data of

Cadmium and Mercury had been obtained by transmission grating, in which

interference and diffraction are dominant phenomena.

Gases in the electric discharge tube had been first made to glow by electric current

flowing through them. Light originated at a spatially limited regions traveled to a

diffraction grating. Light arriving at the slits was coherent light, since it originated at

nearly the same place and time, making possible observation of steady interference

pattern. Every extremely narrow slit then functions as line like sources of light

emerging in cylinder-symmetric manner. This is because of phenomenon called

diffraction, which is the bending of light or other waves as they pass by objects.

Hundreds of cylinder-symmetric wavelets then started to interfere with each other. In

essence, lights from single source split, traveled different parts and recombined by

superposition of electric fields and magnetic fields. If light paths differ by an integer

multiple of the wave length, then when they recombines, they are in phase with each

other, resulting in constructive interference. Similarly, if light paths differ by an odd

integer multiple of a half wavelength, they come together 180° out of phase, resulting

in destructive interference.


Figure 1. Path difference of light traveling from two slits

In grating system, path length difference of lights traveling from two consecutive slits

to the screen equals ��(�), since r1 and r2 appear parallel as slit spacing d becomes

diminutive compared to distance L between slits and the screen. Consequently, angular

positions of bright fringes are indicated by the following equation, with integer m

denotes the order of fringes:

��(�) = �� Equation 1

Light emerging from slits consists of certain wavelengths of discrete frequency.

Equation above indicates that rezoth order maximums of all wavelengths peak together

at the central maximum. For values of m different from zero, the angular position of

the principal maximums is dependent of the wave length. Therefore, diffraction grating

in effect diffracts individual wavelength into unique angular locations, dispersing light

emitted by atom of certain element into its component wavelengths or colors being

observed as spectral line.


II. EXPERIMENT PROCEDURE

Figure 2. Equipment used in experiment: Discharging tube, A grating, A movable telescope

Experiment’s equipment included an electric discharging tube, a grating and a movable

telescope, which makes possible the observation of the angle � in the equation 1. After

turned on, the electric discharge tube was placed in front of the open end of the

collimator. As a result, light from the tube was able to travel to the grating, producing

spectral line or interference fringes. Then the telescope is moved so that the central of

the hairline cross on the telescope’s lens aims exactly at the spectral line. The angle

corresponding to the telescope’s orientation was determined with the aid of a

magnifying glass.

Stage one: Low-pressure gaseous Cadmium was made to glow. Cadmium’s known

spectral lines of four characteristic color had been observed. For each color, angular

position of two principal maximum lying to both sides of the central maximum had

been recorded rather than the angular position of two consecutive principal maximum


for the achievement of a more precise value �. The value � determined for each known

color was used to arrive at the value of spacing of slit d by applying equation 1.

Stage two: The unknown spectral line’s properties of mercury had been investigated.

Given the slit spacing d and the then recorded angular position �, the wavelengths of

colors characteristic to Mercury had been achieved.


III. EXPERIMENTAL RESULTS

Experiment with Cadmium’s spectral line

Table 1: Experiment with electric discharge tube filled with diffuse Cadmium gases

�/ �� /° ��/° �/° d/μm

467.82 100.26 68.50 15.88 1.71

479.99 100.74 67.76 16.49 1.69

508.58 101.76 66.75 17.51 1.69

643.85 106.70 62.05 22.33 1.69

Average distance between two consecutive slits:

�� =�� + �� + �� + ��

4= 1.70μm

Density of line on the grating:

� =1

�=

588.24 ��

1��

Experiment with Mercury’s spectral line

Table 2: Experiment with electric discharge tube filled with diffuse Cadmium gases

d/μm ��/° ��/° �/° �/ ��

1.70 98.10 70.50 13.80 405.51

1.70 99.20 69.40 14.90 437.13

1.70 101.10 67.50 16.80 491.35

1.70 103.20 65.50 18.85 549.23

1.70 104.30 64.50 19.9 578.65

1.70 104.50 64.30 20.10 584.22


IV. ANALYSIS

Error calculation

Errors start in the determination of the telescope’s angular orientation:

∆�� = ∆�� = 0.01°

Magnitude of angle �:

� =�� − ��

2

→ ∆� = ��

��∆�� + �

��

��∆�� =

1

2(∆�� + ∆��)

Result:

∆� = 0.01°

Distance between two consecutive slits d:

� =λ

sin (�)

∆� = ��

��∆� = �−

λ. cos (θ)

sin (�)��∆�

Result:

∆�� = 0.06μm

∆�� = 0.06μm

∆�� = 0.05μm

∆�� = 0.04μm

Average value of d:

� =�� + �� + �� + ��

4

→ ∆� = ��

��∆�� + �

��

��∆�� + �

��

��∆�� + �

��

��∆��

→ ∆� =∆�� + ∆�� + ∆�� + ∆��

4

Result:

∆� = 0.05μm

Density of lines on the grating K:

� =1

�

Result:

∆� = 17.30��

1��


→ ∆� = ��

��∆� = �−

1

��∆�

Calculation of λ:

λ = d. sin(θ)

→ ∆λ = ��λ

��∆� + �

�λ

��∆�

∆λ = |sin (�)|∆� + |�. cos (�)|∆�

Result

∆λ� = ∆λ� = ∆λ�

= ∆λ� = ∆λ� = ∆λ�

= 0.03μm

To put all important results in a nutshell:

� = (1.70 ± 0.05)μm

� = (588.24 ± 17.30) ��

1��

Table 3: Experimental property of Mercury's spectral line

λ�/�� λ�/�� λ�/�� λ�/�� λ�/�� λ�/��

405.51± 0.03

437.13± 0.03

491.35± 0.03

549.23± 0.03

578.65± 0.03

584.22± 0.03


Compare experimental result with literature value

Experimentally found property of Mercury’s spectral line is now be compared with

data found in the Internet:

Table 4: Data on Mercury spectral line

λ�/�� λ�/�� λ�/�� λ�/�� λ�/�� λ�/�� λ�/��

404.66 407.78 435.84 491.60 546.07 576.96 579.07

Surprisingly, data may imply that in the experiment, one spectral line had been left

uninvestigated. However, this probability was not the case. The reason for detecting

only six spectral line instead of seven is that the first two wavelength in the table 4 had

it first order principal maximum not clearly separated. That means λ�in the experiment

corresponds to two first value on the table 4. Difference between the experimentally

determined values then can be compared to literature values:

Table 5: Experimental results compared to literature values

λ�/�� λ�/�� λ�/�� λ�/�� λ�/�� λ�/�� λ�/��

405.51 405.51 437.13 491.35 549.23 578.65 584.22

0.2% larger

0.6% smaller

0.3% larger

0.05% smaller

0.6% larger

0.3% larger

0.9% larger

Furthermore, in the experiment the grating of 600 slits/1mm had been used. Hence, the

experimentally determined density of line on the grating K 558.24slits/1mm is 2%

smaller than the value indicated by the manufacturer.


V. DISCUSSION

The gas filling the tube must be in low-pressure states. This is because only when the

gas is sufficiently diffuse does the light from one atom have a good chance of escaping

the gas before interaction with other atoms, making possible the observation of discrete

spectra. The gas may also emits invisible electromagnetic waves, which will then be

diffracted and undergo interference, creating its own pattern of maximum and

minimum fringes.

The inability to detect Mercury’s first order fringes of its first two wavelength can be

explained by resolving power of grating system in the experiment. Obviously, multi-

slit interference had taken place.

Figure 3. Effect of multi-slit grating

If criteria express by equation 1 hold true to two consecutive slit for one wavelength,

then electromagnetic waves of that wavelength emerging from all other slits and

arriving at the point of the same angular position will interfere constructively. This is

because the distance between every consecutive slits is the same. In effect, the angular

position of the principal maximums is independent of the number of slits. In contrast,

the number of minimum and secondary maximum increase as number of slits increases.

In addition, the intensity of the primary maxima increases and their width deceases as


the number of slits increase, whereas the secondary maxima become relatively less

bright.

For N slit grating, wavelets emerging from N slit must somehow recombine in

completely constructive manner at certain angular position. For example, in two slit

system, two waves recombine in completely destructive manner at the angular position

where their travel path differ by half wavelength. In three slit system, three waves will

interfere completely destructively at the angular position where travel path of any

arbitrary two waves differ by �

�λ or

�

�λ. Generally, for destructive interference in a N-

slit system, angular position of a completely dark line is:

��(�) =�

�λ

where m is an integer different from multiple of N.

If we want to observe clearly spectral lines of nearly the same wavelengths λ and λ�,

they need to be sufficiently dispersed. It has been known that spectral lines are merely

Figure 4. Condition for the observation of two spectral line


distinguishable if the maximum of the wavelength λ� corresponds to the first minimum

of wavelength λ. If they get any closer, the two merger as one maximum.

For the principal maximum of the wavelength λ�:

��(�) =��

�λ�

For the minimum of the wavelength λ under the principal maximum of λ�:

��(�) =�� + 1

�λ

Hence: �� λ� = (�� + 1)λ → �� (λ� − λ) = λ →�

�� = ��

Denote ∆λ = λ� − λ,we obtain:

�

∆�= �� Equation 2

The smaller wavelength difference becomes, the bigger it gets the fraction �

∆�. That

means we will be able to detect spectral line of small wavelength difference if we either

observe them with higher order m, or increase the number of slits N on the grating, or

we do both.

In our experiment, Mercury’s two spectral line with properties λ� =

404.66 �� λ� = 407.78 had not been resolved in the first order fringes. Hence

�� <λ

∆λ→ 1� <

404.66

407.78 − 404.66= 129.69

The number 129.69 suggest that in order to detect this two primary maximum

separately, the number of active slits should be at least 130. The number of active slit


in our experiment must less than 130. If we consider 120 slit had been active in the

experiment, we arrive at the width of light arriving at the grating, which is:

� = 120 × � = 120 × 1.7�� = 0.20��

Equation 2 suggests measures to obtain better experimental results. The utilized grating

of the density 600 slits/1mm should be replaced by the grating of higher density. If it

was true that 120 slits had been active, 600slits/1mm grating should be replaced by the

grating of the density ��

�.��= 637��/1�� or more. Another possibility is letting

more light go through collimator to interact with the grating, bringing up the number

of active slits. This is not a certain way to achieve grating system of higher resolve

power, since the light interacting with the grating may become incoherent, making

interference partem impossible. Furthermore, it is not possible to observe the more

dispersed spectral lines of order higher than one, because the movable scope has

moving restriction. Hence, the most effective and certain way to obtain better

experiment results is to acquire grating of higher density.

Diffraction grating makes possible spectral analysis, offering myriad of useful

scientific application. For example, diffraction grating has proofed its usefulness in

investigating the atomic structure of matter, in identifying the chemical component of

a given sample, or even the prediction on a new element. In the past, the unknown

yellow spectral line signature in sunlight during a solar eclipse had been detected by

French astronomer Jules Janssen in 1868 before, giving rise to prediction of new

element named Helium whose formal discovery was made 27 years later. In addition,

diffraction grating is one of the science’s most important tools in investigating the

composition of stars. It also has many other applications in science and technology

such as wavelength selectors for tunable lasers, selective surfaces for solar energy,

masks for photolithography, beam sampling mirrors for high power lasers,

spectrometers in extreme UV and X-ray regions for space optics, metrology, phase

measuring interferometry and pattern recognition,… Indeed, diffraction grating is a

cleaver exploitation of the diffraction and interference property of lights.


VI. CONCLUSION

Transmission grating is a tool that makes possible the observation of unique spectral

pattern characteristic to atom of certain element. In this experiment with transmission

grating, two phenomena, which confirm the wave nature of light and central to much

of physical optics, have been exposed: diffraction and interference.

VII. REFERENCES

Raymond A.Serway and John W.Jewett, Jr. Physics for Scientists and Engineers

with Modern Physics.

Richard Wolfson and Jay M.Pasachoff. Physics with modern physics for scientists

and engineers.


VIII. APPENDICES

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