Answer
The wavelength of the ozone molecule is $1.511\times10^{-11}m$.
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
- Mass of the ozone molecule:
The molecular weight of ozone is $48g/mol$.
$1 mol$ would have $6.022\times10^{23}$ molecules.
So, 1 molecule of ozone would weigh
$(48g/mol)\times\frac{1mol}{6.022\times10^{23}molecules}\approx7.971\times10^{-23}g/molecule\approx7.971\times10^{-26}kg/molecule$
In other words, $m=7.971\times10^{-26}kg$
- Velocity of the ozone molecule: $v=550m/s$
2) Calculate the wavelength of the ozone molecule
$\lambda=\frac{h}{mv}=\frac{6.626\times10^{-34}}{(7.971\times10^{-26})\times550}\approx1.511\times10^{-11}m$
