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Chapter 2 Assignment: Energy levels of the Hydrogen Atom A. Calculations of the energy levels of the hydrogen atom Each energy level n the atom has a specific energy is given by the following equation: E, (wheren=1,2,3,..) where the energy level, Eni sthe energy of level and Zis the atomic number element For hydrogen, Z=1 and the equation becomes 1) The equation above gives the eneroy per E, hydrogen atom The the easier below, converting 179x10 3/atom) mole Hint: Ifthe energy is -2.179x10" will energy become bigger amole atoms? More negative, less negative?) kJ per mo E, 2) Theoreticall of energy levels will focus on the first ten. Using equation you Question above (giving kJ per mole atoms), complete the following table energies nelettron particular energy level. Energy, Quantum Energy inko/mol Number,r 6 7 3 8 4 9 5 10 the energy values it Table below by drawing horizontal line across the y-axis the horizontal example You wil soon to get al he lines nthe traph- the best you can (like least the first levels). Energy (kJ/mol) -1312 kJ/mol n=1 the spacing energy levels as increases? Put this into your graph. B. Calculation the wavelengths the lines the hydrogen spectrum The observed light emitted by of electrons h yhdrogen atoms fromhigher energy levels to lower energy levels Therefore the energy of the photons calculated by Enstial or AE- Em Elo (since the absolute value of interest) To complete the upper half box. use the values calculated in Table to find the change nenergy using the equation above example for an electron going from the second energy level othe first Do all upper halves of the boxes To complete the associated with the energy changes that were the which rearrang 1.196x103 AE(kJ/mol) where N° Avogadro constant, h- Planck speed of light (converted to nm/s) Table 2 n higher) 984 1 2 3 4 5 Part ( Assigament of electronic transitions to wavelengths Using Table from Part assign as many ofte followine you can The first is shown anexample The wavelengths may not exactly mach your calculated ones There will be four left blank these will explained with Table- Table 3 Wavelength Assignment Wavelength Assignment Wavelength (nm) (nm) Assignment now 97.25 410.29 1005.2 102.57 434.17 1094.1 121.57 486.27 1282.2 389.02 656.47 1875.6 397.12 954.86 4052.3 There were four wavelengths above. Transfer them Table4 They are only considers to six energy levels Yo u calculated the energies Table Using Table Table take aguess &t transition Ther do are correct The first one is done for you (without the calculation shown). Table Unassigned Wavelengths AF (kJ/mol) Probable transition (in nm)from Table (Dayar Mower) 389.02 307.5 2

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