set2 - Thewavefunc,on(x...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
The wave func,on ψ(x) Interpreta,on and condi,ons Ψ * (x)Ψ(x)dx=P(x)dx the probability of Fnding the system between x and x+dx Probability (density) must always be posi,ve Ψ * (x)Ψ(x) > 0 Note that the wave func,on itself need not be posi,ve. In fact it is a complex func,on ψ x ( ) = a x ( ) + ib x ( ) = A x ( ) exp i μ x ( ) ( ) i = 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Bohr model of atoms The electron are moving in exact circles around the nucleus The electron centrifugal energy is pushing it away. Electrosta,c aJrac,on brings it in.
Background image of page 2
The Bohr model (one electron system) Basic assump,ons: 1. To keep the electron in circular orbit the radial forces must cancel Radial force: Electrosta,c force: (atom with one electron but nucleus charge Ze) 2. Electrons that are at a sta,onary state do not radiate and have angular momentum mv 2 r Ze 2 r 2 J = mvr = n n = 1,2, 3,. .. = h 2 π h : Planck constant
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Radius of single‐electron atoms from Bohr’s model 1. force comparison 2. Angular momentum condi,on 3. Subs,tu,ng (1) in (2) mv 2 r = Ze 2 r 2 mvr = n v = n mr m n mr 2 r = Ze 2 r n 2 2 mr 2 = Ze 2 r r = n 2 2 Zme 2 a 0 = 2 me 2 (Bohr radius)
Background image of page 4
Ioniza,on energy (I) When the distance between the nucelus and the electron is very large± the electron is dissociated from the proton(s)± and the interac,on energy between the electron and the proton(s) must be zero p e E = 1 2 mv 2 Ze 2 r using the centrifugal/electrostatic force relation mv 2 r = Ze 2 r 2 mv 2 = Ze 2 r E = Ze 2 2 r r →∞ 0
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 20

set2 - Thewavefunc,on(x...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online