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Q.

The position of proton is measured with an accuracy of $\pm 10^{- 11}$ m. If the speed of proton is equal to speed of light (3 x 10⁸ m/s), what is the uncertainty of proton after 1 s?
(h=6.626 x 10^-34)

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a

300 m

b

0.30 $\overset{o}{A}$

c

none of these

d

3.15 x 10³ m

answer is C.

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Detailed Solution

$\begin{array}{l} Δ x \times Δ v = \frac{h}{4 π m} \\ Δ v = \frac{h}{4 π m \times Δ x} \\ ∆ v = \frac{∆ x}{t} t h e r e f o r e \\ \frac{∆ x}{t} = \frac{h}{4 π m \times Δ x} \\ = \frac{1 \times 6.626 \times 10^{- 34}}{4 \times 3.14 \times 1.672 \times 10^{- 24} \times 10^{- 11}} = 3.15 \times 10^{3} m \end{array}$

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