Question

A proton is accelerated to one-tenth of the velocity of light. If its velocity can be measured with a precision ±2%, then its uncertainty in position is:

Answer 1

Answer:

A proton is accelerated to one-tenth of the velocity of light. If its velocity can be measured with a precision ±2%, then its uncertainty in position is:

Explanation:

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Answer 2

Answer:

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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