Question

a proton is uncertainty two 1/10%c if its velocity can be measured with decision of 0.5%. what must be uncertainty in position.?​

Answer 1

Explanation:

velocity of light, C = 3 × 10^8 m/s

velocity of proton, V = C/10 = 3 × 10^7 m/s

uncertainty in velocity, ∆V = 1% of V

= 1/100 × 3 × 10^7 = 3 × 10^5 m/s

now, use formula,

here, h is plank's constant e.g., h = 6.626 × 10^-34 Js , m is mass of proton e.g., m = 1.673 × 10^-27 Kg

so, ∆x = h/4πm∆V

= 6.626 × 10^-34/(4 × 3.14 × 1.673 × 10^-27 × 3 × 10^5 )

= 1.05 × 10^-13 m

hence, uncertainty in position is 1.05 × 10^-13 m

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