p31318notes04a.pdf

p31318notes04a.pdf - 7 lmn(r = eim 2(2l 1(l | m | |m| |m|...

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7 θ θ = + - - θ θ + - + π = φ θ ψ + + - φ + + - φ 0 1 2 ) /( | | | | 0 1 2 ) /( 0 3 0 4 3 3 | | | | 2 . ) (cos sin . times constant , 2 2 ] )! [( )! 1 ( 4 ) (cos sin |)! | ( 2 |)! | )( 1 2 ( 2 ) , , ( 0 0 na Zr L e P e na Zr L e na Zr a n l n Z l n P m l m l l e r l l n na Zr m l m im l l n na Zr l m l m im lmn

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6 Each eigenfunction is uniquely determined by the values of the three quantum numbers lmn , and so the eigenfunction is often (very often) written merely by listing its quantum numbers in a ket , thus > lmn | . Of course, no two functions have the same set of these three quantum numbers. [At least that is true from what we have learned so far. A little later on we shall find that we have missed a small detail from our model and that a fourth quantum number is required to describe an electron completely. You can probably guess what that is going to be.]
5 ) ( ) 1 ( ) ( r R r R l - = - , so that levels with odd l have odd parity, and levels with even l have even parity. Forget about this for the moment, but later on we may need to recall it. Notation Spectroscopists have developed a notation to describe the electron configuration in atoms. Thus: An electron whose motion is described by an eigenfunction with l = 0 is called an s electron l = 1 is called a p electron l = 2 is called a d electron l = 3 is called an f electron I’ll explain the origin of these letters a little later. After f it goes ghik .... , omitting j. An electron with n = 1 and l = 0 is called a 1 s electron. An electron with n = 3 and l = 1 is called a 3 p electron. An electron with n = 4 and l = 3 is called a 4 f electron, usw. We generally list the electron configuration of an atom by listing the n and l values of each electron, and how many there are of each. For example, silicon in its ground state has the electron configuration 2 2 6 2 2 3 3 2 2 1 p s p s s . That means that is has two 1 s electrons, two 2 s electrons, six 2 p electrons, two 3 s electrons, and two 3 p electrons. It is often pronounced “one s squared, two s squared, two p to the sixth, three s squared, three p squared”. Of course it has nothing to do with “squared” or “to the sixth”, and only very careless people pronounce it that way. I am one of them.

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