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Q.

If an electron is travelling at 200 m/s within 1 m/s uncertainty, what is the theoretical uncertainty in its position in $μm$ (micrometer)?

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a

29

b

14.5

c

58

d

114

answer is C.

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Detailed Solution

$Δx \approx \frac{h}{4 πΔp} \approx \frac{h}{4 π \times mΔv}$

$\approx \frac{6.63 \times 10^{- 14}}{4 \times 3.14 \times 9.1 \times 10^{- 31} \times 1}$

$(∵ Δ v = 1 m / s)$

$∴ Δ x = 58 μ m$

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