If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be

Question

If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be (A) (1/4 π ) (B) (v/4 π ) (C) (v/4 π m) (D) (m v/4 π )

Tardigrade Admin · Accepted Answer

Δ x.m.âv≥ (h/4 π ) or λ .m.âv≥ (h/4 π ) or (h/m v)m.âv≥ (h/4 π ) or Δ v≥ (v/4 π )

Q. If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be

$\frac{1}{4 π}$

$\frac{v}{4 π}$

$\frac{v}{4 πm}$

$\frac{m v}{4 π}$

$Δ x . m .∆ v \geq \frac{h}{4 π}$
or $λ . m .∆ v \geq \frac{h}{4 π}$
or $\frac{h}{m v} m .∆ v \geq \frac{h}{4 π}$
or $Δ v \geq \frac{v}{4 π}$

Q. If the uncertainty in the position of a particle is equal to its de-Broglie wavelength, the minimum uncertainty in its velocity should be

4π1​

4πv​

4πmv​