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

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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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Question Type: Memory (964)
Difficulty Level: Easy (1008)
Topics: Structure of Atom (90)
Subject: Chemistry (2512)

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