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

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)

Tardigrade Admin · Accepted Answer

According to Heisenberg's uncertainty principle

Δ x .Δ p = \frac{h}{4 π}

Given,

Δ x = Δ p

(

Δ x =

= uncertainty in position)

(Δ p)^{2} = \frac{h}{4 π}

(Δ p = m \times Δ v)

m^{2} Δ v^{2} = \frac{h}{4 π}

m =

mass

Δ v^{2} = \frac{h}{m ^{2} 4 π}

Δ v = \frac{1}{2 m} \frac{h}{π}

Δ v

= uncertinty in velocity)

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