1 / 14

Fig. 5-1, p. 171

Chap. 5: 3-D Probability Density.  r  | 2 dV = | R(r)Y(  )| 2 dV Probability of finding the electron in the unit volume element: dV = dxdydz = { rd  }{ rsin (  d  } dr | R(r)Y(  )| 2 = Probability per unit volume. |R(r )| 2 (r 2 dr)

drake-vincent
Download Presentation

Fig. 5-1, p. 171

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chap. 5: 3-D Probability Density r|2dV =|R(r)Y()|2dV Probabilityof finding the electron in the unit volume element: dV=dxdydz= {rd}{rsin(d}dr |R(r)Y()|2 = Probability per unit volume |R(r )|2 (r2dr) probability of finding the electron between a distance r and r+dr |R(r )|2 r2 Prob per unit length |Y()|2sin(dd= |Y()|2d probability of finding the electron in the solid angle d=sin(dd |Y()|2 Prob per unit solid angle Fig. 5-1, p. 171

  2. Chap. Solid Angle for a Sphere of Radius r The solid angleddA/r2 = sin(dddV= dr dA(surface area of dV), dA = r2sin(dd A=4πr2(surface area of the sphere)r2 = 4π solid angle portended(projected) by a sphere Solid angle DDA/r2 dA= r2sin(dd Differential Area DW r

  3. Chap. Solid Angle for a Sphere of Radius r The solid angleddA/r2 = sin(dddV= dr dA(surface area of dV), dA = r2sin(dd A=4πr2(surface area of the sphere)r2 = 4π solid angle portended(projected) by a sphere Solid angle DDA/r2 DW Looking through D and thusDA to find the electron r

  4. =Zr/a0 • Recall that the Bohr radii are rn= n2/Za0 Table 5-2, p. 175

  5. Chap 5: Quantum Mechanical Energy levels The Energy Eigen Values are Independent of l and m! Therefore each n level has n, l levels (0,1, ..n-1), each with (2l+1) states and is therefore n2 degenerate. Each (nl) level has (2l+1) m-states and is (2l+ 1) degenerate

  6. Chap 5: y1s~R10( r )Y00(, y2s~R20( r )Y00(, y3s~R30( r ) Y00( Number of Nodes in Rnl(r) (n-l-1): radial nodes langular nodes Y00( = 1/√4π a0 the Bohr is most probable radius Sphere Radius rs Prob < 0.05 of max prob for finding electron at r > rs

  7. Fig. 5-7, p. 201

  8. Contour Map of the LA Basin

  9. Contour Map of the LA Basin Topographical Map of the LA Basin

  10. Chap 5: Angular Momentum Eigen functions Ypz= Ypz Ypy Ypz=Y10~cos() Linear Combinations of Eigen Functions Ypx=(1/√2){Y11 + Y1-1} ~ sin()cos() Ypy=(1/√2){Y11 - Y1-1} ~ sin()sin() Two Degenerate Eigen Functions can always be added to form Two new Eigen functions of The same Eigen Value Ypx=(1/√2){Y11 + Y1-1} Ypy=(1/√2){Y11 - Y1-1}

  11. Chap 5:, 2pz~R20( r )Ypz(, 3pz R31( r )Ypz( Ypz ~ cos(=f( 0.9 0.7 f( 0.5 30 45 60 |Ypz|2~ |cos( r  2pz~R21( r )Ypz( One electron orbital

  12. Chap 5:, 2pz~R21( r )Ypz(, 3pz R31( r )Ypz( Ypz ~ cos( |Ypz|2~ |cos( r  L 2pz~R21( r )Ypz(

  13. Chap 5:, 2pz~R20( r )Ypz(, 3pz R31( r )Ypz( 2pz~R20( r )Ypz( 2pz one electron orbital 2px~R21( r )Ypx( 2px one electron orbital 2py~R21( r )Ypy( 2py one electron orbital

  14. Chap 5: Angular Momentum Eigen functions d-orbital L dzz ~ R32( r ) Y20( L r  r  L  dx2 -y2 ~ R32{Y22 +Y2-2}~cos(2) dxy ~ R32{Y22 - Y2-2}~ sin(2)

More Related