If uncertainty in position and momentum are equal, then uncertainty in velocity

If Uncertainty In Position And Momentum Are Equal Then Uncertainty Chemistry QuestionIf Uncertainty In Position And Momentum Are Equal Then Uncertainty Chemistry Question

If uncertainty in position and momentum are equal, then uncertainty in velocity is :

Options

(a) 1/2m x √(h/π)
(b) √(h/2π)
(c) 1/m x √(h/π)
(d) √(h/π)

Correct Answer:

1/2m x √(h/π)

Explanation:

We known Δp.Δx ≥ h / 4π
or m.Δv.Δx = h / 4π [ .·. Δp = mΔV]
since Δp = Δx (given)
.·. Δp.Δp = h / 4π or mΔv = h / 4π
or (Δv)² = h / 4πm²
or Δv = √ h / 4πm² = 1 / 2 m √ h / π..

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View Comments (2)

  • We Know that, Δx.Δp ≥ h/4π,
    ∵ x = p
    we can find answer with using two formulae,
    first- Δx.Δp ≥ h/4π,
    second- Δx.Δv ≥ h/4mπ.

  • Here, Δx = Δp = y
    According to Heisenberg's uncertainty principle
    Δx*Δp = h/4π
    y² = h/4π
    y = √h/√4π
    y = 1/2 √h/√π
    So p(Momentum) = 1/2 √h/√π = mΔv
    1/2 √h/√π = mΔv
    1/2m √h/√π = Δv
    So ans is..... Δv = 1/2m √h/√π

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