Please use lots of legible English as well as any ...



Please use lots of legible English as well as any necessary mathematics to answer any of the questions on this test. Your goal is to communicate what you know, not just what is the answer to the question. (If you do not know how to answer the question, then restate the question in a way that you can answer it and show what you do know.) Write outlines before you start writing whenever the question involves more discussion than just an explanation of a calculation. Please start a new piece of paper for each question. (And leave room for the staple!)

1. In electron paramagnetic resonance (EPR) we place an atom (or molecule) into a magnetic field. This splits the energy levels of the atom. Then a microwave field induces a transition (i.e. the system absorbs a microwave photon) and the system moves from the lower state to the upper state.

Consider a hydrogen atom in an “s” orbital. (a) What is the value of ms for each state?

(b) Assuming that the magnetic field strength is B = 0.50 T, calculate the magnitude of (E.

(c) From this, calculate the wavelength of the microwave photon that is absorbed in the transition from the lower to the upper state when the magnetic field is on.

2. (For this problem, please ignore any splitting due to the existence of spin.)

The blue line of the Balmer series in hydrogen ( λ = 434.1 nm) is observed to split into three different spectral lines with Δλ= 0.0250 nm between two adjacent lines when placed in a magnetic field B.

a) Start by showing your understanding of the Balmer series. This transition is from what state to what state? Draw a diagram showing the different possible transitions involving these states, the splitting of the states, and label the diagram with ΔE that corresponds to the reasons for the Δλ.

b) What is the value of B?

c) What is the name of this kind of splitting and what is interacting with what that causes this splitting.

3. a) Use the charts from our book and write down the normalized wavefunction (y(r,q,f)) for the ground state of Hydrogen.

b) Set up the calculation to find the probability of the electron at a location with a radius of less than the Bohr radius. (You do not have to solve this, but set it up enough that others could solve it and get the answer.)

c) You know what the energy of an electron in this state should be…so write that energy down and clearly explain how one could use a wavefunction to show that you are correct. That is, how would you calculate the energy of a state.

4. Consider the 5d states of Hydrogen

a) How many different states are there?

b) For each of the different states, separately and clearly state what are the four quantum numbers, the total orbital angular momentum, and the Lz.

c) Which state has the smallest angle between L and the z axis, and what is that angle.

5. Neon (Ne) is an inert gas with 10 electronics. Potassium (K) is an alkali metal with 19 electronics. Copper (Cu) is a metal with 29 electrons. Write out the electronic configuration for each of these three elements.

[pic]

[pic]

[pic]

[pic]

-----------------------

Field off

Field on

(E

[pic]

[pic]

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download