A particle confined in a rigid one-dimensional box of length has an energy level and an adjacent energy level .
a. Determine the values of n and n + 1.
b. Draw an energy-level diagram showing all energy levels from 1 through n + 1. Label each level and write the energy beside it.
c. Sketch the n + 1 wave function on the n + 1 energy level.
d. What is the wavelength of a photon emitted in the transition? Compare this to a typical visible-light wavelength.
e. What is the mass of the particle? Can you identify it?
here, and the energy diagram is given below.
Wavelength is not in visible range and the particle is seem to be proton.
We have given,
we have to find the value of n and n+1.
Since the energy is one dimensional potential box is given by,
Divided the both equation
We have to draw the energy level diagram.
We have to sketch the wave functions.
We have to find the wavelength of the wave.
We know that we can write,
Its is not a visible wavelength.
We have to find the mass of the particle.
This particle can be proton.
Consider a quantum harmonic oscillator.
a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?
b. What happens to the heights of the antinodes of the wave function as |x| increases? Why?
c. Sketch a reasonably accurate graph of the n=8 wave function of a quantum harmonic oscillator.
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