Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 29 - Molecules and Solids - General Problems - Page 855: 47

Answer

The wavelengths $\lambda$ are less than or equal to $3.5\times10^{-7}m$.

Work Step by Step

The minimum-frequency (i.e., maximum-wavelength) photon that enables conduction has an energy equal to the energy gap. $$E_g= hf=\frac{hc}{\lambda}$$ $$\lambda = \frac{hc}{E_g}$$ $$=\frac{(6.63\times10^{-34}J \cdot s)(3.00\times10^8m/s)}{(1.60\times10^{-19}J/eV)(3.6eV)}$$ $$=3.5\times10^{-7}m $$ This is the maximum wavelength that will excite the electron, so the range of wavelengths that work are those less than (or equal to) that.
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