?Note: Answers to all odd-numbered Problems, numbered in blue, can

Chapter 2, Problem 93

(choose chapter or problem)

Note: Answers to all odd-numbered Problems, numbered in blue, can be found in Appendix III. Exercises in the Problems by Topic section are paired, with each odd-numbered problem followed by a similar even-numbered problem. Exercises in the Cumulative Problems section are also paired but more loosely. Because of their nature, Challenge Problems and Conceptual Problems are unpaired.

An electron confined to a one-dimensional box has energy levels given by the equation

\(E_{n}=n^{2} h^{2} / 8 m L^{2}\)

where n is a quantum number with possible values of 1, 2, 3,. m is the mass of the particle, and L is the length of the box.

a. Calculate the energies of the n = 1,n = 2, and n = 3 levels for an electron in a box with a length of 155 pm.

b. Calculate the wavelength of light required to make a transition from n=1 \(\rightarrow\)  n = 2 and from n = 2 \(\rightarrow\)  n=3. In what region of the electromagnetic spectrum do these wavelengths lie?

Text Transcription:

rightarrow

E_n = n^2h^2/8 mL^2