QUANTUM NUMBERS We have assumed circular orbits Then for hydrogen En 1 13 6eV n2 and L n h 2 If you know n you know both energy and angular momentum Only one quantum number 1 Sommerfeld in 1915 considered elliptical orbits For hydrogen atoms with n all same energy But angular momentum will be different maximum for circular orbit minimum for straight line orbit zero Need another quantum number Have principal quantum number n 1 2 3 4 5 2 Now we introduce angular momentum quantum number l 0 1 2 3 n 1 The third quantum number is needed because the electron in a closed orbit is a current loop A current loop gives a magnetic moment Stern Gerlach Experiment showed magnetic moments only in specific directions Introduce the third quantum number magnetic quantum number ml l 1 0 1 l 3 The electron in orbit has a magnetic moment For this another quantum number is needed spin quantum number ms With the four quantum numbers you can describe the complete state of the atom 4 A system is used to identify the state of the atom For an electron in an atom with l 0 is said to be in an s state For an electron in an atom with l 1 is said to be in an p state For an electron in an atom with l 2 is said to be in an d state For an electron in an atom with l 3 is said to be in an e state Thus for l 0 1 2 3 4 5 state s p d e f g 5 PAULI EXCLUSION PRINCIPLE For Hydrogen only one electron Other elements have more electrons PAULI proposed rule that explains chemical behavior of elements IN ANY ATOM NO TWO ELECTRONS CAN HAVE THE SAME SET OF QUANTUM NUMBERS 6 The quantum numbers and their relationship needed to explain the experiments are n 1 2 3 4 5 l 0 1 2 3 n 1 ml l 1 0 1 l ms These relationships and the Pauli Principle will give Hydrogen 1 electron electron state n 1 l 0 ml 0 ms Helium 2 electrons 1st electron 2nd electron n 1 l 0 ml 0 ms n 1 l 0 ml 0 ms 7 Lithium 3 electrons 1st electron 2nd electron 3rd electron n 1 l 0 ml 0 ms n 1 l 0 ml 0 ms n 2 l 0 ml 0 ms Beryllium 4 electrons 1st electron 2nd electron 3rd electron 4th electron n 1 l 0 ml 0 ms n 1 l 0 ml 0 ms n 2 l 0 ml 0 ms n 2 l 0 ml 0 ms etc Review Table 8 1 in Thornton and Rex 8
View Full Document
Unlocking...