Statistical combination of character of wave and particle of electrons results in the following experimental fact: Ni crystal the wave character of electrons comes from movement of large amount of electrons,i.e.,probability of waves in statistics
Statistical combination of character of wave and particle of electrons results in the following experimental fact： the wave character of electrons comes from movement of large amount of electrons, i.e., probability of waves in statistics 。 Ni crystal
o uncertainty principle Heisenberg said that 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·△px=△x·m△v≥h/2π So a more accurate position measurement-by adding together more waves -means the momentum measurement becomes less accurate (and vice versa)
Heisenberg said that 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/2
5.1.3 Schrodinger equation and quantum numbers 1.Schrodinger equation 02Ψ， 02Ψ，02Ψ=- x2 0z2 Ψ：a wave function E:the overall energy of an electror V:the potentialenergy m:the mass of an electron h:Planck's constant x,v,z:the cartesian coordinates
1.SchrÖdinger equation 5.1.3 Schrödinger equation and quantum numbers x, y,z：thecartesian coordinates V： thepotentialenergy E： theoverall energy of an electron Ψ：a wave function m： themass 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n1m(x,y,z) 1 The principle quantum number,n n=1,2,3,. 2The angular momentum quantum number,l 1=0,1,2,.n-1 3The magnetic quantum number,m m=+l,.0.…,-l 4The electron spin quantum number,ms 1 ms m=- 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. E 2.179×1018 J 72 The different values of n corresponds to different electron shells: n=12 3 4 5. K L M N O
• 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 10 2 1 8 n E n • 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…