Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 38 - Quantization - Exercises and Problems - Page 1154: 47

Answer

${\bf \approx 2.0\times 10^{-18}}\;\rm m$

Work Step by Step

We know that the de Broglie wavelength is given by $$\lambda=\dfrac{h}{mv}\tag 1$$ So we need to find the mass of the red blood cell. Recalling that $\rho =\dfrac{m}{V}$, and hence, $m=\rho V=\rho AL$ where $L$ here is the thickness of the cell. $$m=\rho (\pi r^2 )L$$ Plug into (1); $$\lambda=\dfrac{h}{\pi r^2 \rho L v} $$ Plug the known; $$\lambda=\dfrac{(6.63\times 10^{-34})}{\pi (3.5\times 10^{-6})^2 (1100)(2\times 10^{-6})(4\times 10^{-3})} $$ $$\lambda=\color{red}{\bf 1.96\times 10^{-18}}\;\rm m$$
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