Prof Gilbert LECTURE 17 CHEM 1211 10 20 10 Last time Chapter 6 Partial pressure Px and the mole fraction Xx of gas x in a mixture Px Xx Ptotal Molecular speeds and the meaning of a root mean square Ratio of rates of effusion of two gases Behavior of real gases This time Real gases The van der Waals equation incorporates a and b correction factors to the pressure and volume terms in PV nRT the ideal gas equation The correction factor nb is subtracted from the volume term to account for the volume of the molecules that is not compressible empty space A correction factor a n V 2 is added to the pressure term to account for fewer wall collisions and less pressure due to intermolecular interactions These interactions are between pairs of molecules and so depend on the concentration or each As a result the correction factor scales as the square of n V With values of a and b from a reference book the pressure of a real gas can be calculated using van der Waal s equation P a n 2 V nb nRT V2 Chapter 7 Electrons and Electromagnetic Radiation Electromagnetic Radiation Wave like properties single color monochromatic light has a characteristic wavelength and frequency All radiation travels through space at the same speed c 2 998 108 m s which is the product of the wavelength and frequency of the radiation Units on are s 1 or cycles s or Hz c Images on the right show a long wavelength A low frequency wave and a short wavelength B high frequency wave Electromagnetic Spectrum Behavior of light waves Refraction Waves bend when traveling from one medium to another of different density or refractive index Shorter wavelengths bend more than longer ones Line spectra and Fraunhofer s lines Fraunhofer discovered missing lines in the sun s spectrum Kirchoff and Bunsen were able to put back some of the missing lines demonstrating the complementary nature of the absorption and emission of radiation by atoms as shown here for the sodium D lines at 589 0 and 589 5 nm Similar studies identified the elements responsible for most of the lines in the sun s spectrum e g hydrogen One group of Fraunhofer lines could not be produced by any element found on Earth an element 19th century scientists named after the sun helium These experiments proved that atoms absorb and release characteristic quanities radiant energy corresponding to internal electron energy levels inside the atoms Energy Levels Inside Atoms Observations of Johann Balmer showed that there was a pattern to the four wavelengths of visible the light produced by high temperature H atoms where n 3 4 5 or 6 There were other groups of emission lines in the UV and IR that fit a more general version of the above equation The values of n represent discrete electron energy levels within the H atom The three sets of lines that corresponded to n1 1 2 and 3 are the result of the electron in an H atom dropping down to the n 1 2 and 3 energy levels Photons particles of light When the electron in one H atom falls from n 3 to n 2 it emits one photon of 656 nm light The energy quantum of this photon is equal to E h c where h 6 626 10 34 J s The E values c make the value of constant before the brackets really small 2 18 10 18 J so that the Equation 2 becomes In class inquiry What it the energy of one photon of 656 nm light A simpler equation expresses the energy of any particular energy level n in the H atom 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 Sample Calculations 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 nature of light that is it can waves which meant diffraction and Doppler example but also as the photons emitted or individual atoms or particles of light He duality with an equation wavelength of a photon to where h is Planck s constant effective mass of the He then proposed that the orbiting the nuclei of atoms wave like properties in obvious particle like chose as his model standing the motion of a jump rope but circle instead as if the two were tied together To be known dual behave like undergoing shifts for particles e g absorbed by molecules are expressed this relating the its velocity c and m is the photon electrons could also have addition to their properties He waves similar to moving in a ends of the rope stable the circumference of the circle around which the wave travels must be some multiple of the wavelength of the wave