Particle in a Box: an Electron Is Bound in an Infinite

question 34

Multiple Choice

Particle in a box: An electron is bound in an infinite square-well potential (a box) on the x-axis. The width of the well is L and the well extends from x = 0.00 nm to In its present state, the normalized wave function of the electron is given by: ψ(x) =
sin (2πx/L) . What is the energy of the electron in this state? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^{-19 J})

• A) 0.10 eV
• B) 0.052 eV
• C) 0.13 eV
• D) 0.078 eV
• E) 0.026 eV