Question

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

• A. $\Delta x . \Delta P\, \ge\, \frac{h}{\left(4\pi\right)}$
• B. $\Delta x . \Delta\,v \,\ge\, \frac{h}{\left(4\pi m\right)}$
• C. $\Delta E . \Delta t \, \ge\, \frac{h}{\left(4\pi\right)}$
• D. $\Delta E . \Delta x \,\ge\, \frac{h}{\left(4\pi\right)}$

Answer 1

Answer: (D)

From Heisenberg uncertainty principle,
$\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$ ...(i)
or $\Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$
or $\Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$ ...(ii)
This principle is also applicable for pairs like energy-time $(\Delta E \cdot \Delta t)$ and angular moment-angle $(\Delta w \cdot \Delta \theta)$ along with position-moment $(\Delta x \cdot \Delta p)$.
Thus, $\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}$ ...(iii)