4) Construct the Slater determinant for the first excited state of beryllium. l) 5) Construct the...
Consider the excited state wave function for He atom given by the following Slater determinant 1 432,0(1) V3.2,-2B(1) He (1,2)= V2 V3.2,a(2) W32,-2B(2) Here Y 3,2,-and Y3,2,-2 are hydrogenic wave functions (with Z = 2, see the equation sheet). Show that He (1, 2) is an eigenfunction of Î. = Î., +Î.2. What is the eigenvalue? Î.,, ..2, and Î, are the z-components of the orbital angular momentum operators for electrons 1 and 2, and the z-component of the total...
Use the Slater determinant formalism to write the spin-orbital for the ground state of He atom. Prove that the wave function that is obtained for this satisfies the anti-symmetric requirements for fermions.
(14 points) Write Slater determinants for all possible spin states of the first excited state of He (one electron in the 1s orbital, the other in the 2s orbital). Indicate the S (sum of all e spins) and Ms (vector sum of e spins) values of the corresponding wavefunctions. Evaluate the Slater determinants to obtain the total wavefunctions we wrote in class. Hint: The wavefunctions with σ (1,2) and σ (1,2) require two Slater determinants to correctly represent them.
Using the orbital approximation, write a Slater determinant for a ground state lithium atom. Be sure to include the correct but separate spatial and spin components of the wavefunction
Express the Slater determinant (total wave function) for the ground-state configuration of Boron (B) in terms of orbitals such as 1s, 2s, ··· and spins such as and . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Please answer correctly P.CHEM 2 worksheet and show detailed solution. Write the Slater determinant for the ground state of the boron atom. Hints: Remember the normalization constant is (N!) 2. Boron has five electrons, so you should have a 5 by 5 determinant. You can use the ls, 2s, 2px, 2py, and 2pz orbitals. (you will not use all of them),
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!) By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It's a function of both electrons coordinates and remember Z!)
5. (25 pts) An electron is trapped inside a rigid box of length L-0.250nm. a) If the electron is initially in the second excited state, what is the wavelength of the emitted photon if the electron jumps to the ground state? b) The wavefunction for the electron in its first excited state is given by-(x)fsin2m excited state is given by ψ(x)--sin what is the probability of finding the electron in the middle region of the rigid box, srsc) Sketch the...
By ignoring the electron-electron repulsion write down the approximate form of the first excited state of Helium. What is the probability density? (Hint: It’s a function of both electrons coordinates and remember Z!).
A helium atom in an excited state is trapped ina cubical box of side L. The wave function is given by psi (x, y, z) = (2/L) Sin 2 pi x/L sin pi y/L Sin 2 pi z/L Calculate the 2LL 2L probability of finding the atom in the region L/3 < x <2L/3, L/3 <y<2L/3, 0<Z<L/2