 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2025/paper-2/a9/b/solution

There are twelve model conduction electrons in the conventional unit cell. Hence

n = 12/ a^{3} = 3.78495 \times 1 0^{29} m^{- 3}

k_{F} = (3 π^{2} n)^{1/3}, E_{F} = \frac{ℏ ^{2} k _{F}^{2}}{2 m _{e}} .

Numerically,

k_{F} = 2.23783 \overset{˚}{A}^{- 1}, E_{F} = 19.0799 eV .

The six-electron count is the stipulated model; treating transition-metal d states as completely free is an approximation.

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