When atomic emission lines spectra encounters a diffraction grating. the different wavelengths of light are diffracted at different angles (see Figure 2). For a rst order diffraction, the relationship of wavelength and angle of diffraction is described by 7t=dsin0 The value of d (the distance between grating lines) for this experiment is 1.896 x 10*? m. q The angle of diffraction can be measured according to Figure 3, where tan 9 = x/y so 0 = tan'1 (xly) Once the wavelength (A) is determined, the frequency (v) and the energy of the electromagnetic radiation can be determined. Figure 2: Diffraction of light by a grating PROCEDURES Conrm that the light source. meter stick, and grating are congured as shown in Figure 3. The meter stick should be placed so that the light source is aligned with the 50 cm line. The grating should be perpendicular to the light source exactly 100 cm from the 50 cm line of the meter stick. light source EACH student should look through the line position 3 line position grating to observe the spectra. i x One student in the group looking through the grating should direct another student to move the white tabs to designate where the line of interest "appears" relative to the meter stick. The actual distance of each line according to the meter stick should be recorded (i.e.. left lines should be 50 cm. The absolute distance is the grating absolute value of the difference between the actual reading and the center. For example, / \\ an actual reading of 20.0 cm would give an ' ' absolute reading of i20.o 50.0 i = 30.0 cm. DATA Figure 3: Schematic of the experimental setup (not to scale). Average distance Left line Absolute distance Right line Absolute distance reading (cm) from 50.0cm reading (cm) from 50.0 cm from 50.0 cm(=x) at We aim -mitt escm we\". 2Wmmm . ~ - , Rearranging equation #3 al 'ebralcall (on the bottom of page 1) to express nil in terms of the other variables gives: AR\" "H-"Lm 5. Use your answer to #5 and the experimental value of the wavelength to determine nu for the hydrogen green line. Give the decimal value to 3 sig. gs.. then convert to the appropriate integer. Look at Figure 1 closely for assistance if needed. According to your results, the hydrogen green line emission is a transition from n = __ to n = 6. Use your answer to #5 and the experimental value of the wavelength to determine ml for the hydrogen red line. Give the decimal value to 3 sig. gs., then convert to the appropriate integer. Look at Figure 1 closely for assistance if needed. According to your results, the hydrogen red line emission is a transition from n = _to n = 7. .A line in the infrared region is a transition from n = 4 to n = 3. Use equation 3 to calculate the wavelength for this transition (in urn). Figure 1: Energy level diagram for the hydrogen atom. - 65. The corresponding frequency can be calculated from LRH -16 -4- 3 - C = AV (Eqn. 1) Balmer where c = 2.998 x 108 m/s (speed of light), and the energy per series photon can be calculated from E = hv (Eqn. 2) where h = 6.626 x 10-34 J.s (Planck's constant). According to the Bohr and Schrodinger theories of the hydrogen atom, the individual energy levels are described by E = -K?, where n is the principal quantum number and k is a constant (k = 2.179 x 10-18 J). The energy difference between levels is given by EnH - Ent where nH > nL (H = "high" and L = "low"). For the Balmer series, nL = 2. Principal quantum number, n - Energy This difference must be equal to the energy of the emitted photon. Combining this expression with equations 1 and 2 gives: = RH (Eqn. 3) > 1 where RH = K/hc = 1.0974 x 107 m- (the Rydberg constant). CS Scanned with CamScanner