Question

an electron of mass 9.11x10^-31 and a bullet of mass 0.02kgeach has same speed of500m/s measured to an accuracy of 1 part in 10 raised to power 4.calculate the uncertainty determining the position of the objects

Answer 1

Heisenberg principal:-According to this ,the position and velocity of an object moving with a high speed cannot be taken out accurately at any instance....

The uncertainty in their position and momentum will be in a amount whose product can never be less Than,h/4π

∆x×∆p>/=h/4π

∆x×∆m×∆v>/=h/4π

∆x=h/4π∆m∆v

here, in the given.question

h=6.626×10^-34

∆v=1/10^4=10^-4

m=9.1×10^-31(of electron)

m=.02Kg(of bullet)

First case:-Uncertainity in position for electron ...

∆x=(6.626×10^-34)/(4×3.14×9.1×10^-31×10^-4)

∆x=6.626×10^(-34+31+4)/(12.56×9.1)

∆x=(6.626×10)/(12.56×9.1)

∆x=.6m(approx)

Second case:-Uncertainity in position for object

∆x=(6.626×10^-34)/(4×3.14×0.2×9.1×10^-31)

∆x={6.626×10^(-34+31)}/(12.56×1.82)

∆x=(6.626×10^-3)/(12.56×1.82)

∆x=2.7×10^-4

Hence uncertainty in position of electron is 0.6 and uncertainty in position of object is 2.7×10^-4

{hope it helps}