C O N S T R U C T I O N O F I N E X P E N S I V E W E B - C A M B A S E D

O P T I C A L S P E C T R O M E T E R U S I N G I M A G E J F O R Q U A N T I TAT I V E

S T U D I E S

Fernando Soares

The Professional Teacher

Dr. Bodi Michael

Spring 2016

TABLE OF CONTENTS Goals Introduction Theory • Atomic Emission• Spectrograph

Calibration Methods Build your own spectrograph Calibration Result Conclusion

INTRODUCTION • Spectroscopy is an integral part of chemistry and modern

physics, allowing chemists and physics study the structure and properties of atoms. The webcam spectrograph is a low cost research device which enables students to measure electromagnetic spectra as a function of absolute wavelength. Despite their unsophisticated construction and being made from readily available materials such as DVDs, cardboard, tape and glue. The webcam spectrographs can resolve spectral line within 10’s nm resolution and nm accuracy when properly calibrated from a known source.

GOALS: The purpose of this project is to familiarize students with the optical

workings of a spectrometer and research quality data (which can be obtained from a commercial spectrometer) and also to compare experimental data with theoretical predictions.

Understanding the atomic and molecular structure seeing the real emission spectra in full color as well how to measure wavelengths in the emission-line

Learn to quickly calibrate a spectrometer using a known spectral source, and then use this calibration graph and equation to identify unknown spectral lines

THEORY • Light is electromagnetic radiation. Electromagnetic radiation is

transmitted in a range of waves or particles at different wavelengths and frequencies. This broad range of wavelengths is known as the electromagnetic spectrum.

E=h.γ

λ

Electromagnetic spectrum

λ - Wavelength in nm c- The speed of light in m/sγ - Frequency in s-1

E- is a Energyh - is a Planck’s constant (6.6*10-34 J.s)- is a frequency of the electromagnetic wave

ATOMIC EMISSION SPECTRA• Bohr atomic model predict, that electrons in atoms “are found

in only certain allowed stationary states (lowest energies states possible) with well-defined energies”2.  However, the electrons can be excited to the high energy states (levels) when just the atom absorb the right frequency to generate a photon whose energy equals the energy difference between the states. The electrons then return to lower states initially transited emitting energy in a form of light, with each atom or molecule releasing a single photon of light for each electron energy transition it makes.

Transitional hydrogen atom

• Hydrogen Emission spectrum line (Balmer series for hydrogen Atom )

• Color and shells involved in the downward transition of Balmer series.

SPECTROGRAPH • The spectrograph is a research device which is used to measure the intensity of

electromagnetic radiation at a different wavelength. In its most basic form, the device consists of an opaque barrier with a slit in it (to define the beam of light) a diffraction grating (to split the beam of light into its component colors), and an eyepiece or screen (to allow the user to view the resulting spectrum).

Diffr

actio

n gr

atin

g di

agra

m

Diffraction grating is the heart of the spectrometer, consist of

many parallel evenly spaced mirrored slits on an opaque sheet. The slit spread the light into different color that

make its possible to be measured as function of wavelength .

• The basic function of spectrograph are: A narrow beam of light enters the spectrograph through a small slit in the barrier; the light passes through a diffraction grating and its split into its component colors; the vertical lines is projected onto the screen.

CALIBRATION METHODS • The atomic spectrum will be analyzed by a powerful scientific analysis image

software called ImageJ designed by Wayne Rasband a Special Volunteer at National Institutes of Mental health (NIH) Bethesda, Maryland, USA. ImageJ is public domain open source software, can run as an online applet or as a downloadable application on any computer with a Java 1.5 or later virtual machine.

• Calibration is performed by using statistical models that describe the relationship between dependent and independent variables. Linear regression is a mathematical technique to see deviations from a straight line, fit linear relations and express the relationship between the experimental result and quantities predicted by theory.

• Linear regression is used to study the linear relationship between a dependent variable Y (wavelengths) and independent variables [Distance (Pixels)].

• There is an analytic expression for the slope and intercept and their uncertainties for a straight-line fit, defined by equation Y=bX+a, where a is the y- coordinate intercept, and b is its slope. However, the parameters a and b, of the regression line are estimated from the values of the dependent variable Y(wavelengths), and independent variable X[Distance (Pixels)] with the aid of a statistical model.

BUILD YOUR OWN SPECTROGRAPH Materials needed

The light entrance slit

View port Grating hold piece

G. hold piece folded and shaped with tape

Making a grating from DVD

Grating

Grating attach to the grating holderAlign slit with center of grating

Complete spectrometer

CALIBRATION 1. Take a picture of helium gas with room lamp off.

2. Open ImageJ to convert image to data file

Helium spectral linesHelium gas discharge Plotted intensity against pixels

3. Using data to compare intensity/position to an intensity/ wavelength source available from NIST. Using EXCEL least square fitting algorithm we generated a calibration which calibrated our x pixel value to a wavelength angstrom (and nm).

Pixels Wavelengths

511 3888.6489

541 4026.191

632 4471.479

680 4713.146

721 4921.931

740 5047.74908 5875.6148

1070 6678.1517

1151 7065.1771

400 500 600 700 800 900 1000 1100 12000

1000

2000

3000

4000

5000

6000

7000

8000

f(x) = 4.99519786063792 x + 1327.94150856933R² = 0.999868855008418

Linear regression Calibration -Helium

Distance (Pixels)

Wav

elen

gth(

Ang

.)

Using EXCEL least square fitting algorithm we generated a calibration which calibrated our x pixel value to a wavelength angstrom (and nm).

RESULT • Used a linear fit configuration against 650 nm red laser to test calibrations.

648nm

• We found our peak values of intensity appeared at 648nm which lets us estimate our accuracy of +/-2nm and a resolution of approximately +/- 80 nm from the full width at half height.

• Using Calibration to analyze the hydrogen emission comparing with Balmer hydrogen emission lines theory

Hydrogen spectral lines obtain with spectrometer

Theoretical   Observed λ(nm) Color

Shells Involved λ(nm) Color

656.4 Red 3→2 651.8 Red

486.1 Blue (cyan) 4→2 482.9 Blue (cyan)

434.2 Blue 5→2 430.9 Blue

410.2 Violet 6→2 . Violet

Our calibration present an error of 0.041144 % off the expected value which mean that could be used to identify unknown elements with certain accuracy.

100 200 300 400 500 600 700 80005

1015202530354045 Hydrogen Sample

Wavelenght(nm)

Inte

nsity

(Gra

y va

lue)

651.8nm

CONCLUSION • An inexpensive cardboard visible spectrometer has been constructed and found

to be a useful tool for teaching spectroscopy to high school and undergraduate students. The web-cam based spectrometer yielded quantitative wavelength measurements that agreed well with theory to +/- 2 nm accuracy and +/- 80 nm resolution. The measurement of the wavelength of highest pixels number of the hydrogen spectral line is 0.041144% off by the expected value. The inexpensive nature of the device, costing an order of magnitude less than comparable commercial devices, makes it an appealing option for supplying spectrometers to large physics and chemistry classes for use in laboratory experimentation or in resource-limited educational settings.

REFERENCE LIST • 1- Chaisson, E., & McMillan, S. (2005) Astronomy Today. 5th ed. Upper Saddle River, New Jersey 07458 • 2- Ferreira T., & Rasband W. (2012) ImageJ User Guide (IJ 1.46r Revised edition) Retrieved from

https://imagej.nih.gov/ij/docs/guide/user-guide.pdf• 3- Hughes, I.G., & Hase,T.P.A.( 2010). Measurements and their Uncertainties. A Practical Guide to Modern Error

Analysis. Oxford University Press inc., New York.  • 4- Harris, R. (1998). Modern Physics. 2nd ed. • 5- Introduction to spectroscopy- Physics & Astronomy • http://www.phy.olemiss.edu/Astro/Ex_IndoorLab.pdf• 5- Lucas, J. (2015, March 12). What Is Electromagnetic Radiation? LiveScience Retrieved from  

http://www.livescience.com/38169-electromagnetism.html• 6- Physics, C. () Bohr’s Theory of the Hydrogen Atom. Retrieved from • http://philschatz.com/physics-book/contents/m42596.html• 7- Redd, N. (2013, November 26). Make Your Spectroscope| Spectroscopy Science Fair Project. Livescience

Retrieved from • http://www.livescience.com/41548-spectroscopy-science-fair-project.html• 8- Schneider, A., Hommel, G., & Blettner, M., (2010). Linear Regression Analysis. Journal Deutsches Arzteblatt

107(44): 776-782. doi: 10.3238/arztebl.2010.0776. Retrieved from, • http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2992018/• 9- Stark, G.(2011) Optical Spectrum; Visible radiation; Visible spectrum. ENCYCLOPEDIA BRITANNICA Retrieved

from  • http://www.britannica.com/science/light/Unpolarized-light#toc258433• 10- Stacy, Palen …et. al. (2012). Understanding our Universe (1st ed.)