Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 6 - Electronic Structure of Atoms - Exercises: 6.48

Answer

The wavelength of the muon is $0.397nm$.

Work Step by Step

*The de Broglie relationship: $$\lambda=\frac{h}{mv}$$ $\lambda$: wavelength of object $h$: Planck's constant ($h=6.626\times10^{-34} J.s$) $m$: mass of object $v$: velocity of object 1) Find the known variables - Velocity of the muon: $v=8.85\times10^5cm/s=8.85\times10^3m/s$ 2) Calculate the mass of the muon - Mass of the electron: $9.109\times10^{-31}kg$ - Mass of the muon: $m=206.8\times(9.109\times10^{-31}kg)\approx1.884\times10^{-28}kg$ 3) Calculate the wavelength of the muon $\lambda=\frac{h}{mv}=\frac{6.626\times10^{-34}}{(1.884\times10^{-28})\times(8.85\times10^3)}\approx3.974\times10^{-10}m\approx0.397nm$
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