Prof Gilbert LECTURE 19 CHEM 1211 10 25 10 Last time Chapter 6 Behavior of real gases and van der Waals equation depends on intermolecular interactions the a term and the volumes that molecules occupy the b term Chapter 7 Electromagnetic radiation and the energy inside atoms Wavelike properties of radiation Prisms and raindrops separate sunlight into rainbows by refraction Fraunhofer lines are the result of atomic absorption hot atoms emit the same colors that are missing in the Fraunhofer lines Balmer discovered a periodicity in the wavelengths and energies of the lines in the hydrogen spectrum This time Sample Calculations Energy levels inside atoms Consider how the value of E changes as we go from n 1 2 3 to The lowest most negative energy state is the one for n 1 it s called the ground state All others are excited states These excited states are not stable Within a fraction of a second an electron in one falls to a lower energy state The energy it loses could be emitted as a characteristic wavelength of radiation How much energy does it take to ionize a hydrogen atom that is in the n 2 excited state C O Equation 1 can be used to calculate the energy difference between two energy levels states in an H atom When an electron is ionized n and so the electron is has no atomic energy A If we insert n1 2 and n2 into Equation 1 we get the value of the energy difference between the two states which is the energy we would need to add to ionize the atom S T The energy value is positive because n2 n1 and because we have to add energy to pull the negatively charged electron away from the positive proton in the nucleus Matter waves The above model of an electron orbiting the nucleus of a hydrogen atom in one of many discrete energy levels at characteristic distances from the nucleus is known as the Bohr Model There were two major objections to it when Bohr proposed it 1 it only works for H atoms or single electron ions 2 it defies the laws of physics an electron circling a positive charge should interact with the field produced by the charge lose velocity and spiral into the nucleus In the early 1920 s DeBroglie proposed a solution to problem 2 He started with the well known dual nature of light that is it can behave like waves which meant undergoing diffraction and Doppler shifts for example but also as particles e g the photons emitted or absorbed by individual atoms or molecules are particles of light He expressed this duality with an equation relating the wavelength of a photon to its velocity c where h is Planck s constant and m is the effective mass of the photon He then proposed that the electrons orbiting the nuclei of atoms could also have wave like properties in addition to their obvious particle like properties He chose as his model standing waves similar to the motion of a jump rope but moving in a circle instead as if the two ends of the rope were tied together To be stable the circumference of the circle around which the wave travels must be some multiple of the wavelength of the wave Next step Quantum Mechanics Many scientists refused to buy into Bohr s model or DeBroglie s matter wave rationalization of it They wanted a more rigorous mathematical model In 1927 Erwin Schr dinger produced what the critics were looking for when he derived equations called wave functions that could be used to describe the motion of electron waves Shortly thereafter Max Born proposed that 2 defined the regions around the nuclei of atoms where electron densities were the highest regions called orbitals Wave functions yield sets of numbers called quantum numbers which identify and describe orbitals There are three kinds of quantum numbers and each orbital has a unique combination of the three like the seats at Fenway Park that are each defined by a unique combination of section row and seat The three kinds of quantum numbers are 1 2 3 Principal quantum number n which indicates the relative energy of an orbital and its distance to the nucleus that is its electron shell Angular momentum quantum number l indicates the shape of an orbital Orbital designations l 0 1 2 3 s p d f Magnetic quantum number ml indicates the orientation of an orbital To visualize the possible values of quantum numbers consider the following array of railroad tracks These images show how the distribution of electrons in different orbitals changes with increasing distance from the nucleus States with larger values of n have maxima farther from the nucleus Note s orbitals also have secondary maxima that are closer separated by nodes of 0 density This means that s electrons penetrate closer to the nucleus and feel more of the nuclear positive charge than electrons in a p orbital in the same shell Therefore s electrons have slightly lower energy than p electrons in the same shell