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The position of both, an electron and a helium atom is known within 1.0 nm. Further the momentum of the electron is known within 5.0 × 10⁻²⁶ kg ms⁻¹. The minimum uncertainty in the measurement of the momentum of the helium atom is

1. 50 kg ms⁻¹
2. 80 kg ms⁻¹
3. 8.0 × 10⁻²⁶ kg ms⁻¹
4. 5.0 × 10⁻²⁶ kg ms⁻¹

Correct answer: 5.0 × 10⁻²⁶ kg ms⁻¹

Solution

The uncertainty in position (Δx) and momentum (Δp) are related by Heisenberg's uncertainty principle: Δx × Δp ≥ h/4π. Since the position uncertainty is the same for both the electron and helium atom, the minimum uncertainty in momentum for the helium atom is the same as that of the electron, i.e., 5.0 × 10⁻²⁶ kg ms⁻¹.

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