Chemistry 2720 Fall 2000 Assignment 7

Due: Tuesday, Nov. 14, 9:25a.m.

1.

(a)

Derive an equation for the energy levels of a particle confined to a ring of radius r. [10 marks]

(b)

This might be a (very) crude model for the $\pi$ electron system of benzene. Benzene has six $\pi$ electrons confined to a hexagon of radius 1.4Å. Because of the Pauli exclusion principle, each orbital (energy level) can hold two electrons so the lowest three energy levels are filled. Calculate the wavelength of the transition from the highest occupied orbital to the lowest unoccupied orbital. [6 marks]

2.

The atomic emission spectrum of a light atom can contain lines corresponding to its hydrogenic ion. Give the wavelengths and colors of a few of the visible lines of Li²⁺. Confine your attention to lines involving transitions between levels with principal quantum numbers of 10 or less. [10 marks]

3.

The emission spectrum of hydrogen has a line at 410.2nm. To what transition does this line correspond? [8 marks]