A group of chemistry and physics students are studying the states of the Hydrogen atom.a) Determine all states corresponding to the principal quantum number n=2, giving the n,l andml values for each.b) Calculate the energies of these states.c) What is the maximum angle between the angular momentum and the z-axis?

(a) How many angles can L make with the z-axis for an l=2 electron? (b) Calculate the value of the smallest angle.

The valence election of potassium is excited to a 5d state, (a) What is the magnitude of the election's orbital angular momentum? (b) How many states are possible along a chosen direction?

Vibrations of the hydrogen molecule H2 can be modeled as a simple harmonic oscillator with the spring constant k=1.13103N/m and mass m=1.671027kg. (a) What is the vibrational frequency of this molecule? (b) What are the energy and the wavelength of the emitted photon when the molecule makes transition between its third and second excited states?

What is the difference in energy between the nx=ny=nz=4 state and the state with the next higher energy? What is the percentage change in the energy between the nx=ny=nz=4 state and the state with the next higher energy? (b) Compare these with the difference in energy and the percentage change in the energy between the nx=ny=nz=400 state and the state with the next higher energy.

2. Question 2: a. In your schematic of the hydrogen atom, draw the transition of the electron from the n=1 level to the n=2 level. Label whether the electron gains or loses energy in this transition? 1 b. Find the energy difference between the n=1 level and the n=2 level. Relate this value back to Q1 to make sense of whether the n=1 level or the n=2 level is the lowest energy state. 1/3

a) How many distinct angles from the vertical axis can the orbital angular momentum vector L make for an electron with l = 7? b)Calculate the smallest possible angle the L can make with respect to the vertical axis. (Hint: The smallest angle occurs when ml takes the maximum allowed value. Sketch L in that case and compare the vertical component, which is related to ml, to the magnitude of L, which is related to l.)

a. As a multiple of ħ, what is the angular momentum of a d electron? b. What is the maximum z-componet of angular momentum of a d electron? c. Is (L-)max greater than, less than, or equal to L? 2.

2. a) Problem 8.3 of Textbook: Calculate the frequency of the hydrogen transition n = 101 → n = 100. b) A light photon emitted from a higher energy level ofn = 3 to a lower energy level of n = 2 in hydrogen has a wavelength of 1 = 656.3 nm. Compute the atom distribution ratio N3/N2 at the equilibrium when temperatures are T = 102K.

c. n= 2, 1 = 0. 2. Calculate the maximum number of electrons that can occupy a shell with (a) n = 2, (b) n = 3, and (c) n as a variable. Note you are only looking at the orbitals with the specified n value, not those at lower energies.