Subjective Type

$$(a)$$ What maximum light wavelength will excite an electron in the valence band of diamond to the conduction band? The energy gap is $$5.50 eV$$. $$(b)$$ In what part of the electromagnetic spectrum does this wavelength lie?

Solution

(a) Since the electron jumps from the conduction band to the valence band, the energy
of the photon equals the energy gap between those two bands. The photon energy is given by $$hf = hc/\lambda $$, where $$f$$ is the frequency of the electromagnetic wave and $$\lambda $$ is its wavelength. Thus, $$Eg = hc/\lambda$$ and
$$\lambda =\frac{hc}{E_g}=\frac{(6.63\times 10^{-34}J.s)(2.998\times 10^8 m/s)}{(5.5eV)(1.60\times 10^{-19}J/eV)}=2.26\times 10^{-7}m=226nm$$
Photons from other transitions have a greater energy, so their waves have shorter
wavelengths.
(b) These photons are in the ultraviolet portion of the electromagnetic spectrum.

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