What is the energy (E) for an electron in its ground state (n=3) in a potential well with a width of 15 pm? What is the wavelength of the light required to excite the electron to n=4?

A. E = 12.09 eV, Wavelength = 97.3 nm
B. E = 0.85 eV, Wavelength = 2.44 nm
C. E = 5.11 eV, Wavelength = 243 nm
D. E = 8.48 eV, Wavelength = 155 nm

The energy and wavelength for electron in a quantum well can be calculated considering potential energy of well and quantum energy levels, but the problem lacks specific values to reach a definitive answer.

Explanation:

Given is an electron in its ground state (n=3) in a potential well with a width of 15 pm. The question asks for the energy and the wavelength of the light necessary to excite the electron to n=4. To calculate the energy of the electron we must consider the potential energy within a potential well and the respective energy levels. To calculate the wavelength of light required to move from n=3 to n=4, we must consider the energy difference and use the Planck-Einstein relation, E = hc/λ, where E is the energy difference, h is the Planck’s constant and c is the speed of light.

Unfortunately, the problem lacks some vital data and exact calculations cannot be carried out. Without clear values, we cannot select a correct answer from the options A, B, C, and D.

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