Page 12 - GALIET PHYSICS BLOSSOMS IV+

1.2: Superpositions can also be discussed between states in potential wells. Let’s consider a simple potential well, modeling the electron energy in a single atom of He, which is 10 eV deep in energy, and has a spatial extent of 1˚A. Assume that an electron has a ’ground state’ in this well with an energy of 1 eV above the bottom of the well (ie., 9 eV below the top of the well), and also assume that we can treat this potential well as a square well.
1.2 (a): Draw a diagram of this potential well and show the 3 lowest energy levels for the electron in this well, along with their energies. Suppose we formed a superposition of the ground state and the first excited state – what is the energy difference between these states, in eV units?
• One He atom
• 10 Electronvolt deep in energy
o one electron volt is equal to 1.602176565(35)×10−19 J.
• Spatial extent 1˚A = 1 Angstromà0.1 nm or 10-10m or 100 pm.
• Assume:
o electron’s ground state = 1 electronvolt above the well’s bottom, or 9eV below the well’s bottom o potential well = square well
• each atom has two electrons bound to the He nucleus (2 protons + 2 neutrons) by a strong electrostatic attraction causing a single potential well as shown above, which is very narrow given that the radius of the He atom is so small. So, small radius, small potential well.
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Helium Atomàground state. Nucleusà2 Protons/2 Neutrons 2 electrons orbiting
Negative electrons cancel positive protons.
Electrons now are in electron clouds as seen below.