Answer:
[tex]\Delta x = 1.807 \times 10^{-10}m[/tex]
Explanation:
mass of proton, m = 1.67 x 10^-27 kg
speed of proton, v = 350 km/s = 350,000 m/s
Momentum of proton, p = mass x speed
p = 1.67 x 10^-27 x 350000 = 5.845 x 10^-22 kg m /s
uncertainty in momentum, Δp = 0.1 % of p
Δp = [tex]\frac{0.1\times 5.845 \times 10^{-22}}{100}=5.845 \times 10^{-25}[/tex]
According to the principle
[tex]\Delta x\times \Delta p \geq \frac{h}{2\pi }[/tex]
where, Δx be the uncertainty in position
[tex]\Delta x\times 5.845 \times 10^{-25}= \frac{6.634 \times 10^{-34}}{2\times 3.14}[/tex]
[tex]\Delta x = 1.807 \times 10^{-10}m[/tex]
