Solution Found!
Consider a particle of mass m confined in a
Chapter 31, Problem 86GP(choose chapter or problem)
Consider a particle of mass \(m\) confined in a one-dimensional box of length \(L\) In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length \(L\) that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the linear momentum of the particle are
\(P_{n}=\frac{n h}{2 L} \quad n=1,2,3, \ldots\)
and (b) the allowed energies of the particle are
\(E_{n}=n^{2}\left(\frac{h^{2}}{8 m L^{2}}\right) \quad n=1,2,3, \ldots\)
Equation Transcription:
Text Transcription:
m
L
L
P_n = frac{n h}{2 L} n = 1,2,3, …
E_n = n^{2}(frac{h^{2}}{8 m L^{2}}) n = 1,2,3, ...
Questions & Answers
QUESTION:
Consider a particle of mass \(m\) confined in a one-dimensional box of length \(L\) In addition, suppose the matter wave associated with this particle is analogous to a wave on a string of length \(L\) that is fixed at both ends. Using the de Broglie relationship, show that (a) the quantized values of the linear momentum of the particle are
\(P_{n}=\frac{n h}{2 L} \quad n=1,2,3, \ldots\)
and (b) the allowed energies of the particle are
\(E_{n}=n^{2}\left(\frac{h^{2}}{8 m L^{2}}\right) \quad n=1,2,3, \ldots\)
Equation Transcription:
Text Transcription:
m
L
L
P_n = frac{n h}{2 L} n = 1,2,3, …
E_n = n^{2}(frac{h^{2}}{8 m L^{2}}) n = 1,2,3, ...
ANSWER:
Solution 86GP
Step 1 of 3
Here, we have to derive the expression for the momentum and energy for a particle in a box.
a)