 Solution

ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/section-a/a5/solution

The infinite square well levels for width

L

are

E_{n} = n^{2} h^{2} / (8 m_{e} L^{2})

. Starting in the ground state, the smallest excitation is

1 \to 2

, and its electric-dipole matrix element is nonzero. It therefore sets the longest absorption wavelength:

\frac{h c}{λ _{m a x}} = E_{2} - E_{1} = \frac{3 h ^{2}}{8 m _{e} L ^{2}}, L = \frac{3 h λ _{m a x}}{8 m _{e} c} ≃ 0.302 nm .

The corresponding energy separation is about

12.4 eV

. Elastic scattering of light is a different process from the stipulated absorption into an excited well state.

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