This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Number of Orbitals and Orientation in Space : Each orbital in a particular subshell is specified by m l (the magnetic quantum #). In a given subshell, possible values for m l are:  l, (1  l ), (2  l ) ... 0 ... ( l 2), ( l  1 ), l Therefore 2 l + 1 orbitals in a particular subshell. Each of the orbitals within a particular subshell contributes a portion of the total angular momentum of that subshell. Examples of Electron Probability Density Calculations Each orbital is defined by the appropriate combination of quantum #s. If n = 1, l = 0, m l = 0 it is an sorbital. Such an orbital is radially symmetric so the angular wavefunction Y does not depend on the spherical polar coordinates (therefore a constant). (Refer to eq 17 & 19.) 2 ( r ) = [ R(r)Y ] 2 = e2r/ a(0) / a 3 Max value when r = 0 (nucleus). Decreases to insignificant level at r = 250 pm. However we know that electron is not in the nucleus. Discrepancy is rectified by the radial distribution function. Orbitals specified by l = 0, m l = 0 are sorbitals. The radial wavefunction component of is R(r) . This component has max value when r = 0. It goes to zero as r increases. Radial Distribution Function Gives the probability of the presence of an electron at any position within a spherical shell of radius r and thickness r . Does not depend on spherical polar coordinates, so only the R(r) portion of the (, , r ) wavefunction is needed . P ( r ) = r 2 [ R ( r )] 2 For the sorbital: R(r) = 2er/ a(0) /( a ) 3/2 Another way to express this function is below [ ( , , r ) is the wavefunction for the ground state of the H atom] P(r) = 4 r 2 [ ( r )] 2 Only includes the R(r) portion of . Goes to zero at r = 0. Peak for 1 s orbital corresponds to: r = a = 53 pm. Difference Between Probability Density Predicted by 2 and Predicted by Radial Distribution Function [(, , r )] 2 gives the probability of the electron being in a volume V at a site specified by r and the polar coordinates. P(r) gives the probability of the electron being in a spherical shell of radius r and thickness r. [ (, , r 29 ] 2 is max at the nucleus ( r = 0) then decreases as r increases. P(r) is zero at the nucleus because the volume of the spherical shell becomes zero there (the 4 r 2 in front of 2 in the equation on previous pg goes to zero). A plot of P(r) as a function of r gives the most realistic portrayal of the electron density in each energy level. For an sorbital in the n = 1 Energy Level: Both l and m l are zero. P(r) is max at r = 53 pm ( Bohr radius, a ) then decreases with further increase in r (because 2 goes to zero). Orbital Wavefunctions in Subshells Specified by l = 1 If n > 2 then l can be > 1. The l = 1 subshell contains three porbitals designated by m l = 1, 0 or +1, or by the names: p x , p y or p z ....
View
Full
Document
This note was uploaded on 04/24/2008 for the course CHEM 6A taught by Professor Pomeroy during the Fall '08 term at UCSD.
 Fall '08
 Pomeroy
 Chemistry

Click to edit the document details