The energy gap between the ground state (n=0) and the first excited state (n=1) of an electron in a deep rectangular potential well of width 1Å is calculated using quantum mechanics principles. The energy levels can be determined using the formula E_n = (n²π²ħ²)/(2mL²), where ħ is the reduced Planck's constant, m is the mass of the electron, and L is the width of the well. For a well of 1Å, the energy gap is significant, illustrating the quantization of energy levels in confined systems.
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