Which of the following relationships of Heisenberg, are correct?
$I . Δ P \cdot Δ x \geq \frac{h}{4 π}$
$II . Δ E \cdot Δ t \geq \frac{h}{4 π}$
$III . Δ λ \cdot Δ x \leq \frac{- λ^{2}}{4 π}$
$IV . Δ V \cdot Δ x \geq \frac{h}{4 π m}$

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An Intiative by Sri Chaitanya

I, II and IV only

I, II. III and IV

I and IV only

II and III only

answer is D.

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Detailed Solution

The correct relationship are,
$I. Δ P \cdot Δ x \geq \frac{h}{4 π}$

$II. E = \frac{P^{2}}{2 m}$

$Δ E = V \cdot Δ P$

$V = \frac{Δ x}{Δ t}$

$Δ P \cdot Δ x = Δ E \cdot Δ t$

$III. P = \frac{h}{λ};$

$Δ P = - \frac{h}{λ^{2}} Δ λ$

Hence, option D is correct.

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