PHYSICS 220
Lab 11: Atomic Spectra

Introduction:  In this experiment we will use a diffraction grating optical spectrometer to study atomic spectra. In the first exercise we will observe the spectral lines of mercury and use the known wavelengths of these spectra to calibrate the grating spectrometer.  In the second exercise, we will use the calibrated spectrometer to observe and measure the spectral lines of hydrogen.  From the data we will make two independent determinations of the Rydberg constant.

Background:  The diffraction grating provides the simplest and most accurate method for measuring wavelengths of light. It consists of a very large number of fine, equally spaced, parallel slits, usually thousands of lines (slits) per centimeter. This experiment uses a transmission-grating replicated on plastic.

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


where m is called the order of the spectrum, λ is the wavelength, d is the spacing between grating lines, and θ is the diffraction angle measured with respect to the direction of the light incident on the grating.

When the light from a gas discharge tube is observed with a spectrometer, the colored images of the entrance slit appear as bright lines separated by dark regions: hence, the name line or discrete spectra. Each gas emits photons with a particular set of wavelengths which result in the characteristic spectrum of the gas. The discrete lines of a given spectrum depend on the atomic structure of the atoms and are due to electron transitions. The line spectrum of hydrogen was explained by Bohr's theory that describes spectral lines as resulting from electron transitions between energy levels. However, before that, the line spectrum of hydrogen was shown to follow the description of Balmer's empirical formula:


Here, n refers to the principal quantum number of the initial energy level, and R is Rydberg's constant with a value of R = 1.097 x 107 m-1.  In this experiment, the hydrogen line spectrum will be observed and the wavelengths measured in order to determine the Rydberg constant.

The apparatus: Make yourself familiar with the parts of the spectrometer.

Make sure the printing is pointing up.  Grab the diffraction grating with fingers on your left hand and the plastic around the slit with your right hand.  These two points determine a line and this line should point to the light source you want to analyze.

Hold the spectrometer horizontal.  Look through the diffraction grating and slit at the light source.

Without moving the spectrometer, look to the left of the slit.  You should see two numbered scales: in eV and nm. 

With this spectrometer you will only be viewing the first order (m=1) lines produced by the grating.

MERCURY SPECTRUM

(Relative Intensity versus Wavelength in nm)

 

Exercise 1: Calibration

Procedures: Measure and record the wavelengths (nm) of the five major first order (m = 1) lines of the mercury spectrum. Refer to the diagram above for the wavelengths of these mercury lines. 

Analysis: In an Excel spreadsheet enter the accepted values of the wavelengths in one column and the values you measured in the next column.  Subtract the two columns and calculate an average wavelength correction Δλ that you will need to add or subtract in order to correct your future measurements.

Exercise 2: Hydrogen spectra

Procedures:  Replace the mercury source with the HYDROGEN light source. The hydrogen spectrum observed is the visible part of the so-called Balmer series in hydrogen. The wavelengths of lines in this series are known to obey the Balmer formula (see Background information). Record the values for the wavelengths of the blue, aqua and red lines.  You may also be able to see a violet line. The accepted values for these lines are: violet (410 nm), blue (434 nm), aqua (486 nm), and red (656 nm). 

Analysis: Tabulate the reciprocal of your measured wavelengths.  Correct them using the value you obtained in Exercise 1.  Make a column next to these corrected wavelengths that contains 1/n2 for each line using n = 3, 4, 5, and 6 for the red, aqua, blue, and violet lines, respectively. Using as large a scale as possible, graph the three 1/l values you measured as ordinates against the corresponding values of 1/n2 as abscissas. Choose the best straight line through the data using linear regression.  Use linest to determine the 90% confidence intervals for the slope and intercept.

Discussion: According to the Balmer formula, a plot of this data should yield a straight line with a slope equal to the Rydberg constant R. Compare your slope determination to the accepted value of  R = 1.097 x 107 m-1.

Also, according to the Balmer equation, 1/l tends to a maximum value of R/4 as n gets very large. Obtain a second determination of the Rydberg constant from the intercept and compare it to the accepted value as well.