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Question
The band gap between the valence and the conduction bands in zinc oxide (ZnO) is 3.2 eV. Suppose an electron in the conduction band combines with a hole in the valence band and the excess energy is released in the form of electromagnetic radiation. Find the maximum wavelength that can be emitted in this process.
Solution
Given:
Band gap = 3.2 eV
As the electron in the conduction band combines with the hole in the valence band, the minimum energy band gap (because maximum energy is released) through which the electron has to jump will be equal to the band gap of the material.
This implies that the maximum energy released in this process will be equal to the band gap of the material.
\[\text{ Here }, \]
E = 3 . 2 eV
\[\text{ Thus, }\]
\[ \Rightarrow 3 . 2 \text{ eV } = \frac{1242 \text{ eV - nm} }{\lambda}\]
\[ \Rightarrow \lambda = 388 . 1 \text{ nm }\]
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