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Question: The position of proton is measured with an accuracy of ± 10<sup>–11</sup> m. If the speed of proton ...

The position of proton is measured with an accuracy of ± 10–11 m. If the speed of proton is equal to speed of light (3 × 108m/s), what is the uncertainty of proton after 1s ? (h = 6.626 × 10–34 )

A

300 m

B

0.30 Å

C

3.15 × 103 m

D

None of these

Answer

3.15 × 103 m

Explanation

Solution

Dx0 × Dv = h4πm\frac{h}{4\pi m}

Dv = h4πm×Δx0\frac{h}{4\pi m \times \Delta x_{0}}= Δxt\frac{\Delta x}{t}

Dx =th4πm×Δx0\frac{th}{4\pi m \times \Delta x_{0}}

=1×6.626×10−244×3.14×1.672×10−24×10−11\frac{1 \times 6.626 \times 10^{- 24}}{4 \times 3.14 \times 1.672 \times 10^{- 24} \times 10^{- 11}}= 3.15 × 103 m