Solveeit Logo
Login

Question

Chemistry Question on Structure of atom

Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle?

A

Δx.ΔP ≥ h(4π)\Delta x . \Delta P\, \ge\, \frac{h}{\left(4\pi\right)}

B

Δx.Δ v ≥ h(4πm)\Delta x . \Delta\,v \,\ge\, \frac{h}{\left(4\pi m\right)}

C

ΔE.Δt ≥ h(4π)\Delta E . \Delta t \, \ge\, \frac{h}{\left(4\pi\right)}

D

ΔE.Δx ≥ h(4π)\Delta E . \Delta x \,\ge\, \frac{h}{\left(4\pi\right)}

Answer

ΔE.Δx ≥ h(4π)\Delta E . \Delta x \,\ge\, \frac{h}{\left(4\pi\right)}

Explanation

Solution

From Heisenberg uncertainty principle,
Δx⋅Δp≥h4π\Delta x \cdot \Delta p \geq \frac{h}{4 \pi} ...(i)
or Δx⋅mΔv≥h4π\Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}
or Δx⋅Δv≥h4πm\Delta x \cdot \Delta v \geq \frac{h}{4 \pi m} ...(ii)
This principle is also applicable for pairs like energy-time (ΔE⋅Δt)(\Delta E \cdot \Delta t) and angular moment-angle (Δw⋅Δθ)(\Delta w \cdot \Delta \theta) along with position-moment (Δx⋅Δp)(\Delta x \cdot \Delta p).
Thus, ΔE⋅Δt≥h4π\Delta E \cdot \Delta t \geq \frac{h}{4 \pi} ...(iii)