Chapter XXII Atomic Structure

Rutherford (also Geiger-Marsden)Experiment (1911):Measured angular dependence of  particles (He ions) scatteredfrom gold foil.The results:• Mostly scattering at small angles. But…• Occasional scatterings at large angles(even 90o) Something massive in there !Conclusion: Most of atomic mass isconcentrated in a small region of the atomRecall some history:
Nội dung trích xuất từ tài liệu:
Chapter XXII Atomic Structure GENERAL PHYSICS III Optics & Quantum Physics Chapter XXII Atomic Structure§1. Hydrogen atom§2. Angular momentum of electron§3. Electron spin§4. Many-electron atomsAt present it is well known for you that The Atom - electrons confined in Coulomb field of a nucleus Recall some history: Au Rutherford (also Geiger-Marsden)  Experiment (1911): v Measured angular dependence of  particles (He ions) scattered  from gold foil. The results: • Mostly scattering at small angles. But… • Occasional scatterings at large angles (even > 90o )  Something massive in there ! Conclusion: Most of atomic mass is concentrated in a small region of the atom a nucleus!Early sugession for the quantum nature of atoms: Discrete emission and absorption spectra: (nm) • When excited in an electrical discharge, atoms emitted radiation only at discrete wavelengths • Different emission spectra for different atoms. Atomic hydrogen This could not be explained by classical physics. -e FThere is also a BIG PROBLEM with the classical picture: +Ze As the electron moves in its circular orbit, it is ACCELERATING  radiates electromagnetic energy  would continuously lose energy and spiral into the nucleus (in about 10 -9 sec). We must apply QUANTUM MECHANICS to ATOMS U(r)§1. Hydrogen atom: r1.1 Potential energy of the electron 0 in the hydrogen atom: atom 2 e U ( r )  1 r    9 Nm 2 / C 2 9 10 4 0   (r) U 2 e This potential function implies• Make a test: f    2 actually the Coulomb force r r between the electron & the nucleus • The origin of coordinate system is at the center of mass of   the system (nucleus & electron). • U depends on r, but not on directions in the space. r z y Such a potential is called spherically symmetrical. • The problem is 3-D. Due to the spherical symmetry x   it is more convenient to use the spherical coordinates, than Cartersian. 1.2 The time independent SEQ:  d 2 (x) 2 • Recall 1-D time independent SEQ: 2  ( x) x)   x) U ( E ( 2m dx • The 3-D time independent SEQ is as follows:   2( x ) ( x ) ( x )  2  2 2     2   2  2  U ( x , y , z ) E   2m  x y z  • For the hyrdrogen atom, the potential function U(x,y,z) = U(r) , and the SEQ in the spherical coordinate system is 2   2   1 r  1     1   2  2   2     r sin     sin   2 2   ( r ) E  U 2m   r  r r    r sin     2  2 e Solving and finding the eigenvalues for E and the U ( r )  r eigenfunctions ψ requires some mathematical preparation. In our course of general physics, we will conc ...