Show that the penetration distance has units of .
The penetration distance has units of is given below in step.
We need to find the penetration distance has units of .
The equation of penetration distance is given as:
The unit of is . Its dimension can be .
The unit of is , so dimension is .
The unit of is , then dimension is
Therefore, the dimension of is:
Then, has the dimension of length. So its unit is .
Consider a particle in a rigid box of length L. For each of the states and :
a. Sketch graphs of . Label the points and .
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than . Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box
Model an atom as an electron in a rigid box of length , roughly twice the Bohr radius.
a. What are the four lowest energy levels of the electron?
b. Calculate all the wavelengths that would be seen in the emission spectrum of this atom due to quantum jumps between these four energy levels. Give each wavelength a label to indicate the transition.
c. Are these wavelengths in the infrared, visible, or ultraviolet portion of the spectrum?
d. The stationary states of the Bohr hydrogen atom have negative energies. The stationary states of this model of the atom have positive energies. Is this a physically significant difference? Explain.
e. Compare this model of an atom to the Bohr hydrogen atom. In what ways are the two models similar? Other than the signs of the energy levels, in what ways are they different?
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