I need to write a Atomic Spectra - RESULTS

Atomic Spectra

Learning Goals: 1. You will verify the atomic spectral lines of hydrogen in the Balmer Series. 2. You will apply previously learned diffraction techniques in a new experimental setting

Introduction:

Analysis of spectral signatures are used in all branches of sciences. Spectral data can help scientists determine the make-up of molecules, find minerals on distant planets, and determine reactions in chemistry. In many laboratories spectral analysis is performed not with one's eyes but by relatively simple to sophisticated laboratory equipment. Spectral lines are seen as peaks in graphs and not colored lines by the eyes. In today's lab we will analyze data gathered with a spectrophotometer. The atomic spectra of helium and hydrogen are scanned using a spectrophotometer that measured light intensity as a function of the angle. As light passes through the diffraction grating, the light bends to form a diffraction pattern. The angles to the maxima in the diffraction pattern are given by dsin = m (1) Where d is the separation between the lines on the grating, is the wavelength of the light, and m is the order number. The beam is collimated with the aid of a lens so that the angles are the same for the entire grating. Figure 1: Hydrogen Spectrum c 2 Light is given off by an atom when an excited electron decays from a higher energy orbit to a lower energy orbit. The energy levels of the electron in a hydrogen atom are given by E = ( mee 4 8o 2h2 ) ( 1 n2 ) (2) where me is the mass of the electron, e is the charge of the electron, o is the permittivity constant, h is Planck's constant, and n is the energy level number (1, 2, 3, ...). Plugging these numbers into Equation (2) gives E = (13.6 eV) ( 1 n2 ) (3) The energy of the photon, E, is the negative of the loss of energy of the electron and is given by E = (Ef Ei) = (13.6eV) ( 1 nf 2 1 ni 2). (4) Figure 2: Ray diagram c Figure 3: Bohr atom c 3 For the visible photons given off by hydrogen, the final energy level is = 2. The wavelength, , of the photon given off is determined using = c f (5) where c is the speed of light and f is the frequency: f = E h (6) We can also predict the wavelengths of the Balmer series with an empirically found equation; 1 = ( 1 2 2 1 2 ) (7) In equation (7) R is a constant referred to as the Rydberg constant and equal to 1.097 x 107 m-1 and n is the energy level the electron occupies before deexciting to the n=2 shell level. Experiment: This experiment is done with a spectrophotometer as shown in Figure 4. Figure 4: Spectrophotometer with collimating lens c 4

Experimental Procedure and Data Analysis:

The spectrophotometer uses a collimating system consisting of a slit plate, a converging lens, a grating, mounted on a rotating table, a focusing lens and a light sensor. The slit plate creates single rays. It is placed in the focal point of the lens. The refracted rays coming from the lens are parallel and go through the diffraction grating which is mounted on a rotating table. The second converging lens focuses the rays on a light sensor. The starting position for the ray table is the angle at which the diffraction maximum or center fringe can be seen. It has the highest intensity. Each spectral line will be seen at a different angle. The light sensor is connected to the PASCO interface and the intensity of the spectral lines is recorded as a function of the table angle.

Answer theses

1. Determine the grating line separation. The grating has 600 lines per mm.

2. Analyze the recorded helium spectrum. Using the smart tool measure the table angle for each line and calculate the wavelength of each line. Record the values in a table in excel. The table should be similar to the one in Capstone. Compare your measured wavelength with the actual one. What is the percent difference? Is it reasonable? What would you need to change in the procedure to get more accurate results?

3. Repeat the procedure in step 2 for hydrogen and compare the measured values with the actual values of the hydrogen spectral lines.

4. For each of the wavelengths you found for the hydrogen lines, calculate the energy of the photon using Equations (5) and (6). 5. Now, using these energies, calculate the number of the initial energy level from which the electron decayed from when it emitted each of the photons using Equation (4)

6. Use you measured wavelengths with equation (7). Create a graph of 1/ vs. 1/n2. Insert a trendline and display the equation. What is the slope? Compare the value of the slope with R and calculate the percent difference.