{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# set2 - Thewavefunc,on(x...

This preview shows pages 1–7. Sign up to view the full content.

The wave func,on ψ(x) Interpreta,on and condi,ons Ψ * (x)Ψ(x)dx=P(x)dx the probability of finding 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

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

View Full Document
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.
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

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

View Full Document
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)
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

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

View Full Document
Ioniza,on energy (II)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern