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

Δ x \cdot Δ p \geq \frac{h}{(4 π)}

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Δ x \cdot Δ v \geq \frac{h}{(4 π m)}

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Δ E \cdot Δ t \geq \frac{h}{(4 π)}

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Δ E \cdot Δ x \geq \frac{h}{(4 π)}

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Solution

The correct option is D $Δ E \cdot Δ x \geq \frac{h}{(4 π)}$
From Heisenberg uncertainly principle,
$Δ x \cdot Δ p \geq \frac{h}{4 π}$ ..... (i)

or, $Δ x \cdot m Δ v \geq \frac{h}{4 π}$

or, $Δ x \cdot Δ v \geq \frac{h}{4 π m}$ ...... (ii)

This principle is also applicable for pairs like energy-time $(Δ E \cdot Δ t)$ and angular moment-angle $(Δ w \cdot Δ θ)$ along with position-moment $(Δ x \cdot Δ p)$ .

Thus, $Δ E \cdot Δ t \geq \frac{h}{4 π}$ ..... (iii)

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