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Chapter 9: Problem 68

What is the longest wavelength for a photon that can excite a valence electron into the conduction band across an energy gap of \(0.80 \mathrm{eV} ?\)

Short Answer

Expert verified
The longest wavelength for a photon that can excite a valence electron into the conduction band across an energy gap of 0.80 eV is approximately 1550 nm.

Step by step solution

01

Convert energy from eV to Joules

The energy \(E\) given is \(0.80\) eV. To convert it into joules, we use the relation \(1\) eV = \(1.6 * 10^{-19}\) Joules: \(E = 0.80 * 1.6 * 10^{-19} = 1.28 * 10^{-19}\) Joules.
02

Use Planck-Einstein relation to find frequency

The Planck-Einstein relation is given by \(E = h*f\). Solve for \(f\): \(f = E / h = 1.28 * 10^{-19} / 6.626 * 10^{-34} = 1.93 * 10^{14} s^{-1}\).
03

Convert frequency to wavelength

The relation between frequency and wavelength is given by \(c = f*λ\). Solve for \(λ\): \(λ = c / f = 3 * 10^8 / 1.93 * 10^{14} = 1.55 * 10^{-6} meters = 1550 nm\).

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