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Q.

Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also true. This is summed up in what we now call the Heisenberg uncertainty principle.  The equation is Δx⋅Δ(mv)≥h4πThe uncertainty in the position or in the momentum of a macroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electron is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity isIf the uncertainty in velocity and position is same, then the uncertainty in momentum will beWhat would be the minimum uncertainty in de-Broglie wavelength of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is 722nm?

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answer is [OBJECT OBJECT], [OBJECT OBJECT], [OBJECT OBJECT].

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Detailed Solution

Δx Δp=h4π⇒Δp2=h4π⇒m2Δv2=h4π⇒Δv=12mhπΔx =h4πm;             Δx  Δp=h4πh4πmΔp=h4π,       Δp=mh4πλD.B.=1506Ao=5Aoand Δx⋅hλ2×Δλ≥h4π⇒1π×10−9λ2×Δλ>14π ⇒Δλ≥2.54×10−10Δλ≥0.625Ao
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Werner Heisenberg considered the limits of how precisely we can measure the properties of an electron or other microscopic particle. He determined that there is a fundamental limit to how closely we can measure both position and momentum. The more accurately we measure the momentum of a particle, the less accurately we can determine its position. The converse is also true. This is summed up in what we now call the Heisenberg uncertainty principle.  The equation is Δx⋅Δ(mv)≥h4πThe uncertainty in the position or in the momentum of a macroscopic object like a baseball is too small to observe. However, the mass of microscopic object such as an electron is small enough for the uncertainty to be relatively large and significant. If the uncertainties in position and momentum are equal, the uncertainty in the velocity isIf the uncertainty in velocity and position is same, then the uncertainty in momentum will beWhat would be the minimum uncertainty in de-Broglie wavelength of a moving electron accelerated by potential difference of 6 volt and whose uncertainty in position is 722nm?