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
$\lambda=\frac{h}{mv}=\frac{6.626\times10^{-34}}{(1.884\times10^{-28})\times(8.85\times10^3)}\approx3.974\times10^{-10}m\approx0.397nm$
