A Construct the wavefunction V(r, 0, ¢) for an H atoms' electron in the state 2pz. Pleasenote that in order to have a real-valued wavefunction of pr orbital(see below), you needto do a linear superposition of the corresponding spherical harmonics for the angularpart. Use the spherical harmonics table below. Show that the superposition you selectedindeed results in a real orbital; however, you do not need to simplify the expressionsfurther or normalize the wavefunction.Px1/2Yg = ()"" (5 cos 0 -3 cos 0)cos e%3D(4x21 1264л/1/2sin e (5 cos? e- 1)eti87-yY =(3 cos²0 – 1)105 1/232sin e cos de2ie(16715 12sin e cos betie35 12(647sin de iB Now consider an excited state of He atom with electron configuration 1s 2s'. In general,the wavefunction is a state:V(r, 0, 0, 02) = V(r,0, ø)V..where V(r, 0, 6) 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, ø)and o (r, 0, ø), 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 written*(r, 0, 4)3*(r, 0, ¢) + 43"(r, 0, ¢)6?*(r, 0, »)v(r, 0, ø) =F(r,0, 6)63"(r, 0, ¢) – 3°(r, 0, ø)0?*(r, 0, ¢)V12(r, 0, ø) =Explain (and demonstrate) which spatial wavefunction (V2(r, 0, ø) or Vī2(r, 0, ø))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, ø), o(r, 0, 6) and spin components of V,, denoted as (†, 4) or (4, 1).

Given: The spherical harmonics which is useful to find the wavefunction for 2px is

A Construct the wavefunction W(r, 0, 4) for an H atoms' electron in the state 2pz. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction.

A Construct the wavefunction W(r, 0, 4) for an H atoms' electron in the state 2pz. Please note that in order to have a real-valued wavefunction of p, orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction.