CSUS Department of Chemistry xperiment 9 Chem. 1A xp. 9 PR-Lab ASSIGNMNT Name: Lab Section (1) Use equation (2) [see the discussion on the next page] to calculate the energies of the ten lowest states for the hydrogen atom, and enter your answers in Table 1. (2) Calculate the energy differences between each pair of the six lowest levels and place them in the upper halves of the appropriate boxes in Table 2. (3) Use equation (1) [see the discussion on the next page] to calculate the wavelength corresponding to each energy difference calculated in part (2). Convert your wavelengths to nanometers and place them in the bottom halves of the appropriate boxes in Table 2. Table 1: nergy Levels of the Hydrogen Atom (from quation 2) Quantum number, n nergy,, in J Quantum number, n nergy,, in J 1 6 2 7 3 8 4 9 5 10 Table 2: Calculated nergy Differences (J) and Wavelengths (nm) for the Hydrogen Atom. (Watch your sig. figs.!) n (lower) 1 2 3 4 5 n (upper) 6 5 4 3 2 Page 1 of 6
CSUS Department of Chemistry xperiment 9 Chem. 1A Name Section ATOMIC SPCTRA INTRODUCTION At room temperature essentially all atoms are in their ground (lowest-energy) electronic state. When heated or placed in an electric discharge, atoms are excited to higher electronic states. Light is then emitted as the atoms relax back to lower energy states. Since atomic energy levels are quantized, not all wavelengths will be emitted. When an atom falls from an upper to a lower energy level, the photon emitted must have the following energy: hc photon = upper lower = (1) where h (Planck s constant) = 6.626076 x 10-34 Jis, c (speed of light in a vacuum) = 2.997925 x 10 8 m/s, and = the wavelength of the photon. For example, a few of the energy levels of the sodium atom are shown below: nergy O (zero) Ionization occurs 3.121 x 10 19 J Level 3 (2 nd excited state) 4.862 x 10 19 J Level 2 (1 st excited state) 8.234 x 10 19 J Level 1 (ground state) The energy of the photon emitted when the sodium atom makes a transition from the first excited state to the ground state is: photon = 4.862 x 10 19 J ( 8.234 x 10 19 J) = 3.372 x 10 19 J The wavelength of the photon is: = 34 8 hc (6.626 x 10 J s)(2.998 10 m / s) = 19 (3.372 x 10 J) photon 9 7 1 10 nm = 5.892 10 m 1m = 589.2 nm This wavelength is in the yellow region of the visible spectrum, which explains the yellow color emitted when glass containing sodium atoms is heated in a flame. A sodium atom can also emit light at two other wavelengths ( 3 1 and 3 2 ) as well as light at many more wavelengths involving energy levels not included in the diagram above. The set of all wavelengths ( lines ) emitted by an atom is known as its atomic spectrum. Since each element has a unique set of electronic energy levels, the atomic spectrum for each element is also unique. As a result, elements can Page 2 of 6
CSUS Department of Chemistry xperiment 9 Chem. 1A readily be identified from their atomic spectra. In the first part of this experiment, you will use a spectroscope to view lines in the visible portions of several atomic spectra. The hydrogen atom has a particularly simple spectrum. According to the Bohr theory, the energy levels of the hydrogen atom are given by the equation R n = (2) 2 n where R = 2.17879 x 10 18 J and n = 1, 2, 3 (any positive integer). The lines in the atomic spectrum of hydrogen are grouped into series, where each member of a series involves a transition to the same lower energy level. In the second part of this experiment you will calculate the energy for the first ten levels of the hydrogen atom, and use these energies to calculate the wavelengths of some lines in several different spectral series. XPRIMNTAL A. Line spectra of elements. Check out a small spectroscope from the laboratory instructor and use it to view the emission spectra from discharge tubes containing hydrogen, helium, neon, and mercury which will be set up in the balance room. Draw a sketch of the lines you see for each element, indicating the colors observed. Label each line in your sketch with its wavelength in nm. B. Hydrogen atom (1) Use Table 2 (from the pre-discussion assignment) to assign quantum numbers to the experimental hydrogen atom spectral lines listed in Table 3. (2) Table 4 contains a few experimental wavelengths which you will not find among your values calculated for Table 2 in your pre-discussion assignment. Determine to which series you think each of these lines belongs, and attempt to assign quantum numbers to each line. Calculate the wavelength corresponding to each of your assignments to verify its correctness. Page 3 of 6
CSUS Department of Chemistry xperiment 9 Chem. 1A DATA AND CALCULATIONS Name: This xperiment is due at the end of lab. Lab Section A. Sketches of Line Spectra (Complete the sketch for hydrogen and any one of the three other elements.) (1) Hydrogen (2) Helium (3) Neon (4) Mercury Page 4 of 6
CSUS Department of Chemistry xperiment 9 Chem. 1A B. Hydrogen Atom Name: This xperiment is due at the end of lab. Lab Section Table 3: Some xperimental Wavelengths (nm) in the Spectrum of the Hydrogen Atom Wavelength n higher n 1ower Wavelength n higher n lower 97.25 410.29 102.57 434.17 121.57 486.27 1094.1 656.47 1282.2 4052.3 1875.6 2625.9 Table 4: More xperimental Wavelengths (nm) in the Spectrum of the Hydrogen Atom xperimental Wavelength (nm) 389.04 397.15 954.90 1005.4 Belongs to series with n lower = n higher upper lower (J) (from Table 1) Calculated Wavelength (nm) QUSTIONS 1. Use the diagram in the Introduction to calculate 3 1 and 3 2 for a sodium atom. xpress your answers in nanometers. 2. (a) Calculate the energy required to ionize a sodium atom from its ground state. (b) How many kilojoules of energy are required to ionize a mole of sodium atoms from their ground states? Compare your result with the value in your text. Page 5 of 6
CSUS Department of Chemistry xperiment 9 Chem. 1A 3. In 1886, Balmer showed that the lines he observed in the visible and near ultraviolet region of the hydrogen atom spectrum had wavelengths which could be expressed by the following equation: 1 1 1 = C n n 2 2 lower upper where C is a constant. (a) Based on your results in Table 2, what is n lower for this group of lines, now known as the Balmer series? (b) If wavelength is expressed in nanometers, what is the numerical value of the constant C in Balmer s equation? (c) What is the longest possible wavelength for a line in the Balmer series? (d) Calculate the shortest wavelength that a line in Balmer series could have. (e) The lines you sketched in part A for hydrogen belong to the Balmer series. Assign n upper for each line in your sketch. (If you observed a yellow line, ignore it. It arises from sodium atoms in the glass.) Page 6 of 6