Emission Spectrum of Atomic Gases Prelab Questions Before this coming to this lab, please review your text for the physics of the spectrum of visible light and of diffraction grating spectrometer.. Which photon will have the greater wavelength, a photon of green visible light or a photon of red visible light?. Which photon will have the greater energy, a photon of green visible light or a photon of red visible light?. Which photon will diffract over a greater angle, a photon of green visible light or a photon of red visible light?. You are looking for the points of maximum constructive interference from four colors of light, green, red, blue and orange. In what order will you see the colors in your spectrometer if you start at 0 0 (straight on) and rotate clockwise? 5. Assume you are looking at a gas that emits three different wavelengths of visible light; green, orange and red light. If you see constructive interference from red light at 0 0 from straight on, what will you see if you continue to increase the angle? 6. You will use equation () to calculate the wavelength,, based on the angle and the distance between the slits, d. How will you determine the distance between the slits? 7. What is the value for nf in equation ()?
Physics 5 Emission Spectrum of Atomic Gases Overview: In this experiment, we will determine the Rydberg constant using a optical spectrometer and a light source of excited hydrogen gas. Along with this main objective, we will review the emission spectra of helium and mercury. We will be using an optical grating spectrometer to determine the wavelengths of the emission lines. Physics: Light source Focusing lens Grating Rotating eyepiece Figure A simple drawing of a optical spectrometer is shown in Figure. The atomic gases will be placed in an excited state by use of an electrical potential in the light source shown on the left. When the excited electrons return to their ground state, they will emit light at specific frequencies predicted by quantum mechanics. The multi frequency light is focused and passed through a diffraction grating. This grating has been inscribed with over 0,000 small slits per inch. When light passes through each of these multiple slits, it will diffract, causing these grating to act light a source of hundreds of points of light, all in-phase. Constructive interference of all these light sources will cause maxima to appear at different angles on the right side of the grating, depending on the wavelength of the light. The positions of maximum constructive interference will obey the following formula: m sin d eq () These positions of maximum constructive interference will appear as bright lines of difference colors in our spectrometer. By searching for these bright lines with our rotating eyepiece and noting the angle at which they are formed, we can determine the wavelengths that made up the visible portion our light source s spectrum.
Procedure: Place the light as close as possible with the narrow portion of the gas tube by the slit. Adjust the focusing of your eyepiece on the telescope for clean viewing of both the light and cross hairs as viewed through the scope. If the instrument is calibrated properly the alignment of the scope will register 80 on the angular scale, if it aligns above or below the 80 mark you will have to add or subtract this correction from your angular reading. The 80 mark is your zero reference line from which you will be recording angles of respective colors. Moving the scope (pivot) to the left slowly you should begin to see colors of bright lines appearing in your field. Slowly move the scope and its pivoting support so that the cross hairs split the first observed color. (Any line that is observed within 0 of 80 0 is not an indication of constructive interference. You are merely looking directly into the lamp.) Record the angle to the nearest minute of a degree. Keep moving and registering the angles of each color observed on left side. Repeat by moving scope to the right of the zero line. In an ideal situation the same colors and angle displacement should be found on the right side, however, due to human and equipment error this may not be true. Not knowing if the left or right side is more accurate the angle we will use in our equation will be the average of left and right side. Repeat measuring right and left angles for Hydrogen and Mercury. Once all angles are known you are to determine the wavelengths for each observed angle and color. Step - Determining d: Find the green emission line from mercury gas and determine the angle for its first maximum. The known wavelength of this line is 56 angstroms (Å). (Note: Å = 0-0 m = 0. nm.) With this information, determine d and record it at the bottom of the data table. Step Review of Emission Spectra: Continue with Mercury and find the position of all other maxima. Record the colors and angles on the attached table. Calculate the wavelengths. Repeat this for helium and hydrogen. Step Determining the Rydberg constant: The Rydberg constant, R, is used in the formula: R n f n i eq () Based on the above formula, determine the average value of the Rydberg constant from all of your hydrogen data.
Mercury: Line Color Left Angle ( o ) Right Angle ( o ) Aver Angle ( o ) Wavelength (nm) 5 Hydrogen: Line Color Left Angle ( o ) Right Angle ( o ) Aver Angle ( o ) Wavelength (nm) 5 Helium: Line Color Left Angle ( o ) Right Angle ( o ) Aver Angle ( o ) Wavelength (nm) 5 6 7 8 d-spacing of diffraction grating = m
Determination of the Rydberg constant for Hydrogen: Hydrogen: Line Wavelength (nm) ninitial nfinal R (m - ) Average:
Homework ) Based on your table, which observed color for hydrogen has the shortest wavelength? ) Based on your table, which observed color for hydrogen has the greatest frequency? ) Since we are looking at visible light, which frequency series are we looking at? ) For the calculation of the Rydberg constant, we used the light from electrons with the final state of n=. Why didn t we use the electrons with a final state of n=? 5) For the greatest frequency you observed, what is the initial value of n? 6) Do you think the hydrogen gas we used was excited to any states higher than the value of n you listed above? If not, what caused this upper limit on n? If it was excited to higher states, why didn t you observe these lines?