Below is a figure that depicts the potential energy of an electron (a finite square well), as well as the energies associated with the first two wave-functions. a) Sketch the first two stationary wavefunctions (solutions to the Schrődinger equation) for an electron trapped in this fashion. Pay attention to detail! Use the two dashed lines as x-axes. U(x) E2 E1
Below is a figure that depicts the potential energy of an electron (a finite square well), as well as the energies associated with the first two wave-functions. a) Sketch the first two stationary wavefunctions (solutions to the Schrődinger equation) for an electron trapped in this fashion. Pay attention to detail! Use the two dashed lines as x-axes. U(x) E2 E1
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![Below is a figure that depicts the potential energy of an electron (a finite square well), as well as the
energies associated with the first two wave-functions.
a) Sketch the first two stationary wavefunctions (solutions to the Schrődinger equation) for an electron
trapped in this fashion. Pay attention to detail! Use the two dashed lines as x-axes.
U(x)
E2
E1
b) If the potential energy were an infinite square well (not finite well as shown above), what would the
energy of the first two allowed energy levels be (i.e., E1 and E2). Write the expressions in terms of
constants and a (the width of the well) and then evaluate numerically for a = 6.0*10-10 m. [If you don't
remember the formula, you can derive it by using E = ħ²k² /2m, together with the condition on 1 =
2a/n.]
c) Let's say I adjust the width of the well, a, such that E1 = 3.5 eV. In that case, calculate the wavelength
(in nanometers) of a photon that would be emitted in the electron's transition from E2 to E1.
(Remember: hc = 1240 eV nm]
b) In this same infinite square well (from part c), how many states (or energy levels) are there below an
energy ceiling of 200 eV? Given the Pauli exclusion principle, how many electrons would fit into those
states?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F390feb3e-0bb0-40d3-b7a2-7ecd43bc3c8a%2F850f38be-068b-4b68-9906-65737833f71a%2F041cwip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below is a figure that depicts the potential energy of an electron (a finite square well), as well as the
energies associated with the first two wave-functions.
a) Sketch the first two stationary wavefunctions (solutions to the Schrődinger equation) for an electron
trapped in this fashion. Pay attention to detail! Use the two dashed lines as x-axes.
U(x)
E2
E1
b) If the potential energy were an infinite square well (not finite well as shown above), what would the
energy of the first two allowed energy levels be (i.e., E1 and E2). Write the expressions in terms of
constants and a (the width of the well) and then evaluate numerically for a = 6.0*10-10 m. [If you don't
remember the formula, you can derive it by using E = ħ²k² /2m, together with the condition on 1 =
2a/n.]
c) Let's say I adjust the width of the well, a, such that E1 = 3.5 eV. In that case, calculate the wavelength
(in nanometers) of a photon that would be emitted in the electron's transition from E2 to E1.
(Remember: hc = 1240 eV nm]
b) In this same infinite square well (from part c), how many states (or energy levels) are there below an
energy ceiling of 200 eV? Given the Pauli exclusion principle, how many electrons would fit into those
states?
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