Supplementary uncertainty principle According to Heisenberg it is impossible to determine simultaneously both the position and velocity of an electron or any other particle with any great degree of accuracy or certainty △x·x=x·mAv≈h So a more accurate position measurement-by adding together more waves-means the momentum measurement becomes less accurate (and vice versa)
According to Heisenberg it is impossible to determine simultaneously both the position and velocity of an electron or any other particle with any great degree of accuracy or certainty So a more accurate position measurement – by adding together more waves – means the momentum measurement becomes less accurate (and vice versa). uncertainty principle x px = x mv ≈ h Supplementary
8.1.3 Schrodinger equation and quantum numbers 1.Schrodinger equation 02Ψ. 02Ψ，02Ψ=- 0x2 y2 0z2 乎：a wave function E:theoverallenergyof an electro I:thepotentiaenergy m:the mass of an electron h:Planck's constant x,v,z:thecartesiancoordinats
1.SchrÖdinger equation 8.1.3 Schrödinger equation and quantum numbers x, y,z：thecartesian coordinates V： thepotentialenergy E： theoverallenergy o f an electron Ψ：a wave function m： the mass of an electron h：Planck's constant (E V) Ψ h m z Ψ y Ψ x Ψ + + 2 2 2 2 2 2 2 2 8 π
2.Quantum numbers 平n1,m(x,y,z) 1 The principle quantum number,n n=1,2,32. 2The angular momentum quantum number,l l=0,1,2,.n-1 3 The magnetic quantum number,m m=+l,.0.…-l 4 The electron spin quantum number,m 1 ms= ms=- 2
2. Quantum numbers ① The principle quantum number, n l 0,1,2,...n1 ③ The magnetic quantum number, m ④ The electron spin quantum number, ms , 2 1 ms m +l,......0......,l 2 1 ms ②The angular momentum quantum number, l n=1, 2, 3,…… ( , , ) , , Ψ x y z n l m
The principle quantum number,n: The value of n determines the total energy of the electron.The energy of the electron in the H atom varies only with the value of n. 2.179×1018 三 J 23 The different values of n corresponds to different electron shells: n=12 3 4 5. K L M NO
• The value of n determines the total energy of the electron. The energy of the electron in the H atom varies only with the value of n. J 2.179 1 0 2 18 n E • The different values of n corresponds to different electron shells: The principle quantum number, n： n = １ ２ ３ ４ ５… K L M N O…
The angular momentum quantum number,I: 1=0,1,2,3...n-1 Each value of corresponds to different types of subshells s,p,d,f...within a shell. I decides the shapes of angular function of y The magnetic quantum number,m: m=0,±1，±2...±1； m is related to the spatial orientation of an orbital in a given subshell
The angular momentum quantum number, l ： l = 0，1，2，3……n－1 Each value of l corresponds to different types of subshells s, p, d, f…within a shell. l decides the shapes of angular function of The magnetic quantum number, m： m= 0，±1, ±2……±l ； m is related to the spatial orientation of an orbital in a given subshell