Answer: The uncertainty in proton's position is [tex]6.307\times 10^{-10}m[/tex]
Explanation:
The equation representing Heisenberg's uncertainty principle follows:
[tex]\Delta x.\Delta p\geq \frac{h}{2\pi}[/tex]
where,
[tex]\Delta x[/tex] = uncertainty in position = ?
[tex]\Delta p[/tex] = uncertainty in momentum = [tex]m\Delta v[/tex]
m = mass of the particle = [tex]1.673\times 10^{-27}kg[/tex]
[tex]\Delta v[/tex] = uncertainty in speed = [tex]0.01\times 10^{4}m/s[/tex]
h = Planck's constant = [tex]6.627\times 10^{-34}kgm^2/s^2[/tex]
Putting values in above equation, we get:
[tex]\Delta x.(1.673\times 10^{-27}\times 0.01\times 10^4)=\frac{6.627\times 10^{-34}kgm^2/s^2}{2\times 3.14}\\\\\Delta x=\frac{6.627\times 10^{-34}}{2\times 3.14\times 1.673\times 10^{-27}\times 0.01\times 10^4}=6.307\times 10^{-10}m[/tex]
Hence, the uncertainty in proton's position is [tex]6.307\times 10^{-10}m[/tex]
