Question

If uncertainty in position and momentum are equal, then
uncertainty in velocity is :
(a) 1/2m√h/π
(b) √h/2π
(c) 1/m√h/π
(d) √h/π

Answer 1

If uncertainty in position and momentum are equal, then

uncertainty in velocity is 1/2m√h/π

Answer 2

answer : option (a) 1/2m √(h/π)

a/c to question,

uncertainty in position and momentum are equal.

means, ∆x = ∆p

using formula, ∆x.∆p = h/4π

[ Heisenberg uncertainty principle, we can't find out position and momentum of subatomic particle simultaneously, minimum error occurs h/4π ]

⇒(∆p)² = h/4π

⇒∆p = √{h/4π}

⇒m ∆v = 1/2√{h/π}

⇒∆v = 1/2m √{h/π}

hence uncertainty in velocity is 1/2m √{h/π}.

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