The 4fz(x2-y2) orbital has the angular function Y = (constant)z(x^2-y^2)/r^3 a. How many radial nodes does this orbital have? b. How many angular nodes does it have? c. Write equations to define the angular nodal surfaces. What shapes are these surfaces?

rue or false? The hydrogen atom has a 3 orbital. Explain.

Do atoms in excited states emit radiation randomly, at any wavelength? Why? What does it mean to say that the hydrogen atom has only certain discrete energy levels available? How do we know this? Why was the quantization of energy levels surprising to scientists when it was first discovered?

which of the following does have the lowest polarizability? Z of I=53, F=9. Br=35, Cl=53

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6. Normalize 2pz orbital a. 2a, e cos e

The pi electrons in an eight-carbon polyene (CH2=CH-CH=CH-CH=CH-CH=CH2) can be modeled as a one-dimensional particle in a box of length 1nm. a. What are the values of the quantum number n for the highest occupied (HOMO) and lowest unoccupied (LUMO) energy level based on the number of pi electrons in this molecule? HOMO n= LUMO n= b. Predict the wavelength of light that would be absorbed in order to induce an electronic transition between the HOMO-LUMO gap. In what region of the electromagnetic spectrum would this transition fall? ΔΕ = λ =

10. (a) Use the radial wave function for the 3p orbital of a hydrogen atom to calculate the value of r for which a node exists. (b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom.

Why is there electron subshell overlap in the 4s and 3d orbitals?

The following questions relate to the wavefunction for the hydrogen-like atom shown in question 1. What does is meant by "hydrogen-like"? Give 5 examples of hydrogen-like species. b. Explain the connection between the wavefunction and atomic orbitals. What are the two components of а. the wavefunction? С. How do the two components of the wavefunction relate to the nodes of the wavefunction?