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

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..

admin:

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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