Q16 / 160 · WBJEE 2012 · Chemistry
Which of the following does not represent the mathematical expression for the Heisenberg uncertainty principle?
- A$\Delta x \cdot \Delta P \geq h /(4 \pi)$
- B$\Delta x \cdot \Delta v \geq h /(4 \pi m)$
- C$\Delta E \cdot \Delta t \geq h /(4 \pi)$
- Correct answerD$\Delta E \cdot \Delta x \geq h /(4 \pi)$
Solution
From Heisenberg uncertainty principle, $\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$
or $\quad \Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$
or $\quad \Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$
This principle is also applicable for pairs like energy-time $(\Delta E \cdot \Delta t) \quad$ and $\quad$ angular $\begin{array}{llll}\text { moment-angle } & (\Delta w \cdot \Delta \theta) & \text { along } & \text { with }\end{array}$
position-moment $(\Delta x \cdot \Delta p)$
Thus,
$$
\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}
$$
Hence, the correct answer is option: 'D'.