First slide
Quantum mechanical model of the atom
Question

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 ΔxΔ(mv)h4π

The 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. 

Moderate
Question

If the uncertainties in position and momentum are equal, the uncertainty in the velocity is

Solution

Δx Δp=h4πΔp2=h4πm2Δv2=h4πΔv=12mhπ

Question

If the uncertainty in velocity and position is same, then the uncertainty in momentum will be

Solution

Δx =h4πm;             Δx  Δp=h4πh4πmΔp=h4π,       Δp=mh4π

Question

What 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?

Solution

λD.B.=1506Ao=5Ao

and Δxhλ2×Δλh4π

1π×109λ2×Δλ>14π Δλ2.54×1010

Δλ0.625Ao


(p=h/λ​ or △p=(h/λ2 ).​△λ)

 

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