Physics: Principles with Applications (7th Edition)

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

Chapter 27 - Early Quantum Theory and Models of the Atom - General Problems - Page 801: 83

Answer

$4.0\times10^{-7}\;\rm W/m^2$ $0.017 \;\rm V/m $

Work Step by Step

According to the description in the problem and according to our previous knowledge, the intensity for photons is the number of photons striking an area of $1.0\;\rm m^2$ per second. Thus, $$I=\dfrac{N}{A}\;E=\dfrac{Nh\nu}{A}$$ where $\nu$ is the frequency. And hence, $$I= \dfrac{Nhc}{A\lambda}$$ Plugging the known; $$I= \dfrac{1\times10^{12}\times 6.626\times10^{-34}\times3\times10^8}{1\times 497\times10^{-9}}$$ $$I=\color{red}{\bf 4.0\times10^{-7}}\;\rm W/m^2$$ Now we need to find the maximum electric field which is given by $$I=\dfrac{\varepsilon_0 c E^2}{2}$$ Solving for $E$; $$E=\sqrt{\dfrac{2I}{\varepsilon_0 c}}$$ Plugging the known; $$E=\sqrt{\dfrac{2\times 4\times10^{-7}}{8.85\times10^{-12}\times3\times10^8}}$$ $$E=\color{red}{\bf 0.017}\;\rm V/m $$
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