An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is . How long is the box?
The longest wavelength in the absorption spectrum is so the box is .
We have to given that the longest wavelength in the absorption spectrum is .
We need to find the length of the box.
Absorbing the photon with the longest wavelength will result in the transition of the electron from the ground state to the state, and that's because the photon with the longest wavelength is the one with the smallest energy, and the smallest energy difference between the two states happens between and states. The energy of levels of an electron in a rigid box is given by:
in order for the transition to take place, the incident photon must have an energy equal to the energy difference between and . Since,
the equation to isolate and substitute the numerical values of the different variables.
a. What is the probability that an electron will tunnel through a air gap from a metal to a STM probe if the work function is ?
b. The probe passes over an atom that is “tall.” By what factor does the tunneling current increase?
c. If a current change is reliably detectable, what is the smallest height change the STM can detect?
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