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ExamsNEETChemistry

Uncertainty in position of an electron (mass = 9.1 × 10⁻³¹ kg) moving with a velocity of 3 × 10⁴ cm/s accurate upto 0.001% will be [use ΔxΔp ≥ h, in uncertainty expression where h = 6.626 × 10⁻²⁷ erg-second]:

  1. 1.93 cm
  2. 3.84 cm
  3. 5.76 cm
  4. 7.68 cm

Correct answer: 3.84 cm

Solution

The uncertainty in velocity (Δv) is 0.001% of 3 × 10⁴ cm/s, which is 3 × 10⁻⁴ cm/s. Using ΔxΔp ≥ h, where Δp = mΔv, we calculate Δx = h / (mΔv). Substituting h = 6.626 × 10⁻²⁷ erg·s, m = 9.1 × 10⁻³¹ kg (converted to g = 9.1 × 10⁻²⁸ g), and Δv = 3 × 10⁻⁴ cm/s, we find Δx ≈ 3.84 cm.

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