Uncertainty in the position of an electron ( mass = 9.1 × 10^-31 kg ) moving with a velocity 300 m/s , accurate up to 0.001\% , will be ( h = 6.63 × 1 - Chemistry MCQ AIEEE 2006 2026 | ExamTest.live

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Uncertainty in the position of an electron (mass = 9.1 \times 1 0^{- 31} kg) moving with a velocity 300 m/s, accurate up to 0.001%, will be (h = 6.63 \times 1 0^{- 34} Js):

Solution & Step-by-step Explanation

Heisenberg's Uncertainty Principle: Δ x \cdot Δ p \geq \frac{h}{4 π} . Δ p = m Δ v .Velocity v = 300 m/s, uncertainty in velocity is 0.001% . Δ v = 300 \times \frac{0.001}{100} = 300 \times 1 0^{- 5} = 3 \times 1 0^{- 3} m/s Δ x = \frac{h}{4 πm Δ v} Δ x = \frac{6.63 \times 1 0 ^{- 34}}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 31} \times 3 \times 1 0 ^{- 3}} Δ x = \frac{6.63 \times 1 0 ^{- 34}}{3.43 \times 1 0 ^{- 32}} \approx 1.92 \times 1 0^{- 2} m

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Uncertainty in the position of an electron (mass = 9.1 \times 1 0^{- 31} kg) moving with a velocity 300 m/s, accurate up to 0.001%, will be (h = 6.63 \times 1 0^{- 34} Js):

19.2 \times 1 0^{- 2} m

5.76 \times 1 0^{- 2} m

1.92 \times 1 0^{- 2} m

3.84 \times 1 0^{- 2} m

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