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# The energy gap, $\Delta E$, for silicon is $110 \mathrm{~kJ} / \mathrm{mol}$. What is the minimum wavelength of light that can promote an electron from the valence band to the conduction band in silicon? In what region of the electromagnetic spectrum is this light?

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Given: Energy gap for silicon, $\Delta$E = 110 kJ/mol

(1) First, calculate for the energy gap of silicon in joules is shown below:

$\Delta\text{E} = (\dfrac{\text{110 kJ}}{\text{mol}}) (\dfrac{\mathrm{10^{3}}\text{J}}{\text{kJ}}) (\dfrac{\text{1 mol}}{\text{6.023 x }\mathrm{10^{23}}})$

$\Delta\text{E = 18.263 x }\mathrm{10^{-20}}\text{ J}$

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