Uncertainty in the position of an electron moving with a velocity of 200 m/s, accurate up to 0.01%, will be: 

CONCEPT:

Heisenberg's Uncertainty Principle

• Heisenberg's uncertainty principle states that it is impossible to simultaneously determine the exact position and exact momentum (or velocity) of a particle.
• The uncertainty in position (Δx) and momentum (Δp) are related by:

  Δx × Δp ≥ h / 4π

  where h is Planck's constant (6.626 × 10^-34 J·s).
• Momentum (p) is given by:

  p = m × v

  where m is the mass and v is the velocity.
• Uncertainty in momentum (Δp) can be calculated as:

  Δp = m × Δv

  where Δv is the uncertainty in velocity.

EXPLANATION:

• Given:
  • Velocity of the electron (v) = 200 m/s
  • Accuracy of velocity = 0.01%
  • Mass of electron (m) = 9.1 × 10^-31 kg
  • Planck's constant (h) = 6.626 × 10^-34 J·s
• Uncertainty in velocity (Δv):
  • Δv = (0.01 / 100) × 200
  • Δv = 0.02 m/s
• Uncertainty in momentum (Δp):
  • Δp = m × Δv
  • Δp = (9.1 × 10^-31) × (0.02)
  • Δp = 1.82 × 10^-32 kg·m/s
• Uncertainty in position (Δx):
  • Δx × Δp ≥ h / 4π
  • Δx ≥ h / (4π × Δp)
  • Δx ≥ (6.626 × 10^-34) / (4 × 3.1416 × 1.82 × 10^-32)
  • Δx ≥ 2.9 × 10^-3 m

Therefore, the uncertainty in the position of the electron is approximately 2.9 × 10^-3 m.