confusing points!

[ChemSiddiqui]

hi all,

 

just a couple of points I want clarification on;

 

1. Orbitals in many-electron atoms are lower in energy than the hydrogenic orbital.

 

I dont understand this bit. when the principal quantum number increases, the radial function increases, so the energy should infact increases due to increased screening effect. But this statement says the opposite!

 

2. d orbitals are poorly shielded so that nd orbital is of slightly higher energy than (n+1)s orbital for a gasesous element. e.g. ...4s<3d...!

 

I dont get it, when d orbitals are poorly shielded they should be penetrating the core much better than (n+1)s orbital and experience the Zeff more and thus should be lower in energy.

 

can anyone explain these two points please or maybe direct me someplace where I can find the answer.

 

thnx

[amit]

1. Orbitals in many-electron atoms are lower in energy than the hydrogenic orbital.

i think they are talking about corresponding orbitals of hydrogen and other elements. here due to higer charge on nucleus will result in higher attraction hence lower energy. ie 1s e- of other elements will de lower than the 1se- of H similarly 2s,2p... of others will be of lower energy then that of hydrogen.

 

. d orbitals are poorly shielded so that nd orbital is of slightly higher energy than (n+1)s orbital for a gasesous element. e.g. ...4s<3d...!

i dont know as far i have read d orbitals shield poorly. but they are very vell shielded

[vedmecum]

hi all,

 

just a couple of points I want clarification on;

 

1. Orbitals in many-electron atoms are lower in energy than the hydrogenic orbital.

 

I dont understand this bit. when the principal quantum number increases, the radial function increases, so the energy should infact increases due to increased screening effect. But this statement says the opposite!

 

2. d orbitals are poorly shielded so that nd orbital is of slightly higher energy than (n+1)s orbital for a gasesous element. e.g. ...4s<3d...!

 

I dont get it, when d orbitals are poorly shielded they should be penetrating the core much better than (n+1)s orbital and experience the Zeff more and thus should be lower in energy.

 

can anyone explain these two points please or maybe direct me someplace where I can find the answer.

 

thnx

 

up to my knowledge there must be a correction in your statement . d-orbitals are not poorly shielded but they shield poorly . This result in slightly decrease in energy of outer orbitals electron .

 

for energy comparison http://www.chemguide.co.uk/atoms/properties/atomorbs.html

[ChemSiddiqui]

1. Orbitals in many-electron atoms are lower in energy than the hydrogenic orbital.

i think they are talking about corresponding orbitals of hydrogen and other elements. here due to higer charge on nucleus will result in higher attraction hence lower energy. ie 1s e- of other elements will de lower than the 1se- of H similarly 2s,2p... of others will be of lower energy then that of hydrogen.

 

How so?

 

I think from the equation we could solve this problem quantitaively,

 

(schrodinger wave equation cant account for energies due to e-e repulsion);

 

E=- kZ^2/n^2 which describes the dependence of the energy with the principal quantum number. but I cant think of a qualitative answer to this except shielding and penetration. Does 2s or 2p penetrate the nucleus better than the 1s. the radial distribution graph for the 3 orbitals seem to suggests so. If that is, problem solved!

[amit]

well my simple logic was that higher the charge on nucleus higher will be the attraction felt by electron. as electrostatic energy is E=k (Q1*Q2)/r^2

now since considering Q2= charge of electron=-e, hence greater the Q1 more negative hence smaller will be the energy.

and same term can be used in shrodinger equation for P.E

 

http://www.chemistry.mcmaster.ca/esam/Chapter_3/fig3-8.jpg

here it can be seen that lower the n more penetrated it is as most probanle r increases with n. hence 1s is most penetrating