Now consider an excited state of He atom with electron configuration 1s' 2s'. In general,the wavefunction is a state:V (r, 0, 6, 02) = V(r, 0, ø)Vo.where V(r, 0, ø) and V, represent the spatial and the spin part. The spatial part isconstructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, 6)and ø (r, 0, 6), where subscript k denotes which electron it belongs to (i.e., k is either1 or 2 since we have two electrons).• The spatial part of the wavefunction can be written1*(r, 0, 4)o3* (r, 0, 4) + o(r, 0, ¢)o²*(r, 0, 4)V2F (r, 0, 4)«3"(r, 0, ø) – 05" (r, 0, 4)o²°(r, 0, ø)V2V2(r, 0, 6) =Vī2(r, 0, 6) =Explain (and demonstrate) which spatial wavefunction (V2(r, 0, 0) or V2(r, 0, 0))is symmetric with respect to exchange of two electrons? Which one corresponds tothe singlet and triplet state (defined by the spin multiplicity)?• Based on you response to the previous question, write down the wavefunction for the(i) ground state of He and the (ii) singlet excited state of He. Use spatial orbitals(r, 0, 6), (r, 0, 6) and spin components of V, denoted as (†, 4) or (4, 1).

Answered: Image /qna-images/answer/feb9117b-7ce1-4f13-bb24-c94b05f58a76.jpg

Now consider an excited state of He atom with electron configuration 1s' 2s'. In general, the wavefunction is a state: (r, 0, 6, o2) = ¥(r,0, ¢)Vo, where V(r, 0, 6) and Vo, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, 6) and o (r, 0, ), where subscript k denotes which electron it belongs to (i.e., k is either 1 or 2 since we have two electrons). • The spatial part of the wavefunction can be written o(r, 0, ¢)* (r, 0, ¢) + ¢}"(r, 0, ¢)&*° (r, 0, 4) V2(r, 0, ø) = *(r, 0, 6)3"(r, 0, 4) – 63 (r, 0, ø)oF*(r, 0, ¢) Vī2(r, 0, ¢) = Explain (and demonstrate) which spatial wavefunction (2(r,0, ) or V2(r, 0, 6)) is symmetric with respect to exchange of two electrons? Which one corresponds to the singlet and triplet state (defined by the spin multiplicity)? • Based on you response to the previous question, write down the wavefunction for the (i) ground state of He and the (ii) singlet excited state of He. Use spatial orbitals (r, 0, 6), (r, 0, ¢) and spin components of V,, denoted as (†, ) or (t, t).

Now consider an excited state of He atom with electron configuration 1s' 2s'. In general, the wavefunction is a state: (r, 0, 6, o2) = ¥(r,0, ¢)Vo, where V(r, 0, 6) and Vo, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, 6) and o (r, 0, ), where subscript k denotes which electron it belongs to (i.e., k is either 1 or 2 since we have two electrons). • The spatial part of the wavefunction can be written o(r, 0, ¢)* (r, 0, ¢) + ¢}"(r, 0, ¢)&° (r, 0, 4) V2(r, 0, ø) = (r, 0, 6)3"(r, 0, 4) – 63 (r, 0, ø)oF*(r, 0, ¢) Vī2(r, 0, ¢) = Explain (and demonstrate) which spatial wavefunction (2(r,0, ) or V2(r, 0, 6)) is symmetric with respect to exchange of two electrons? Which one corresponds to the singlet and triplet state (defined by the spin multiplicity)? • Based on you response to the previous question, write down the wavefunction for the (i) ground state of He and the (ii) singlet excited state of He. Use spatial orbitals (r, 0, 6), (r, 0, ¢) and spin components of V,, denoted as (†, ) or (t, t).

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom

Section: Chapter Questions

Problem 11.14E

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