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?

The 4fz(x2-y2) orbital has the angular function Y = (constant)z(x2-y2)/r3a. 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?

1. The angular portions of the wave functions for the px and dxz orbitals of the hydrogen atom are linear combinations of the spherical harmonics and are given by the expressions below. 3 YP. = √(x²+x¹) = -sin coso 4T Wd₂ = 1/2 (Y/² + X/₂ ¹) = eigenfunctions of 15 4π These combinations are chosen to yield real functions. Are these functions a Ĺ sincoscoso -iħ. do ?

Why 3D orbital is possible but 3f is not posssible? Explain it.

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

7. Why are the following functions not acceptable wave functions for a 1D particle in a box in the region (0 a)? N is a normalization constant. NTX a. ý = Ncos L b. NTX sin a C. ý = Ntan a

3. The structure of heme molecules is based on a porphyrin ring. We can model these molecules as a particle on a ring where the radius is 440 pm. There are 22 electrons moving in the conjugated ring. In the ground state, each orbital is occupied by 2 electrons. Calculate a) the energy and angular momentum (J) of an electron in the HOMO and b) the wavelength of the transition between the HOMO and LUMO.Yeah

3. Prove that angular momentum of a particle confined to the xy palne is quantized 4. Neutrons have no electric charge, so they do not interact with the atomic electrons. Hence, they are very penetrating (e.g.,typically 10 cm in lead). Neutron diffraction was proposed in 1934, to exploit de Broglie's hypothesis about the wave nature of matter. Calculate the momentum and kinetic energy of a neutron whose wavelength is comparable to atomic spacing (1.8×1010 m)