Respuesta :
Answer: The uncertainty in the velocity of oxygen molecule is [tex]4.424\times 10^{-5}m/s[/tex]
Explanation:
The diameter of the molecule will be equal to the uncertainty in position.
The equation representing Heisenberg's uncertainty principle follows:
[tex]\Delta x.\Delta p=\frac{h}{2\pi}[/tex]
where,
[tex]\Delta x[/tex] = uncertainty in position = d = [tex]4.50\times 10^{-5}m[/tex]
[tex]\Delta p[/tex] = uncertainty in momentum Β = [tex]m\Delta v[/tex]
m = mass of oxygen molecule = [tex]5.30\times 10^{-26}kg[/tex]
h = Planck's constant = [tex]6.627\times 10^{-34}kgm^2/s^2[/tex]
Putting values in above equation, we get:
[tex]4.50\times 10^{-5}m\times 5.30\times 10^{-26}kg\times \Delta v=\frac{6.627\times 10^{-34}kgm^2/s}{2\times 3.14}\\\\\Delta v=\frac{6.627\times 10^{-34}kgm^2/s^2}{2\times 3.14\times 4.50\times 10^{-5}m\times 5.30\times 10^{-26}kg}=4.424\times 10^{-5}m/s[/tex]
Hence, the uncertainty in the velocity of oxygen molecule is [tex]4.424\times 10^{-5}m/s[/tex]
