Question

Which of the following relations is/are correct regarding Hisenberg's uncertainity principle?

• A. Δx. (Δp) ≥ $\frac{h}{2\pi }$
  
• B. Δx. (Δp) ≥ $\frac{h}{4\pi }$
• C. ΔE.Δt ≥ $\frac{h}{2\pi }$
  
• D. ΔE. Δt ≥ $\frac{h}{4\pi }$

Answer 1

Answer: (B), (D)

The correct options are
B Δx. (Δp) ≥ $\frac{h}{4\pi }$
D ΔE. Δt ≥ $\frac{h}{4\pi }$

Δx. (Δp) ≥ $\frac{h}{4\pi }$
$\Rightarrow \Delta x.m.\left(\Delta v\right)\ge \frac{h}{4\pi }$
where Δx = uncertainity in position
Δp = uncertainity in momentum
m = mass of the particle
Δv = uncertainity in velocity
h = Planck's constant
ΔE. Δt ≥ $\frac{h}{4\pi }$
where ΔE = uncertainity in energy
(Δt) = Uncertainity in time