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Choose the Best Answer · Q25

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

(a) Δx⋅Δp≥h4π\Delta x\cdot\Delta p\geq\dfrac{h}{4\pi}
(b) Δx⋅Δv≥h4πm\Delta x\cdot\Delta v\geq\dfrac{h}{4\pi m}
(c) ΔE⋅Δt≥h4π\Delta E\cdot\Delta t\geq\dfrac{h}{4\pi}
(d) ΔE⋅Δx≥h4π\Delta E\cdot\Delta x\geq\dfrac{h}{4\pi}
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Step 1. (a) Δx⋅Δp≥h/4π\Delta x\cdot\Delta p\geq h/4\pi is the standard position-momentum form of Heisenberg's principle - a valid conjugate pair.

Step 2. (b) Δx⋅Δv≥h/(4πm)\Delta x\cdot\Delta v\geq h/(4\pi m) follows directly from (a) by substituting Δp=mΔv\Delta p=m\Delta v - also valid.

Step 3. (c) ΔE⋅Δt≥h/4π\Delta E\cdot\Delta t\geq h/4\pi is the energy-time form of the uncertainty principle, a well-established corollary relating energy and time as another conjugate pair - also valid. …

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