Question

If the uncertainty in velocity and position is same then the uncertainty in momentum would be

Answer 1

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)



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.

Sheethu says:

March 28, 2018 at 2:48 pm

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

Answer 2

Answer:

Heisenberg uncertainty principle =Δx.ΔP

=> =h2

Δx= uncertainty in position

Δp= uncertainty in momentum =mΔV

Let, Δx=Δv=y

So, y2.m=h/4π

y=[h/(4mπ)]1/2

uncertainty in momentum =y.m

=[mh4π]1/2

=12.[mh/π]1/2