## Question

l = 1.

a. What is the length of the angular momentum vector?

b. How many possible Z components are there? List them.

c. What angles does the L vector make with the z-axis?

2. An electron is in the n = 2, l = 1 state. What is

a. The most probable value for the radius?

b. The average (or expectation) value for the radius?

c. The average potential energy?

3. Draw a vector diagram showing the 2 possible orientations of the spin angular

momentum S for an electron. What is the angle between S and the z-axis for these 2

states?

4. Make a table showing the values of the 4 quantum numbers n, l, me, ms and energies for each of the 10 lowest-lying quantum states (not energy levels) of a hydrogen atom.

5. A hydrogen atom in its ground state is placed in a magnetic field B = 0.33 T applied in

the Z direction.

a. What is the energy difference between the spin-up and spin-down states?

b. What frequency of electromagnetic radiation would excite the atom from the lower to upper energy state? Identify the kind of radiation (visible, etc.).

24. Give interpretations of the slope and intercept. Because of the fine-structure splitting of the 3p state the, 3p ---> 3s ransition in sodium actually consists of two closely spaced lines of wavelengths 589.00 nm and 589.59 nm. Assuming a magnetic moment of one Bohr magneton, find the effective magnetic field that produces the fine-structure splitting of the 3p state of sodium.

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