one may say that in dealing with milligram- sized or heavier objects, the associated uncertainties are hardly of any real consequence. In the case of a microscopic object like an electron on the other hand. ∆ v. ∆ x obtained is much larger and such uncertainties are of real consequence.
For example, for an electron whose mass is . × – kg., according to Heisenberg uncertainty principle It, therefore, means that if one tries to find the exact location of the electron, say to an uncertainty of only – m, then the uncertainty ∆ v in velocity would be m s m ms which is so large that the classical picture of electrons moving in Bohr’s orbits (fixed) cannot hold good. It, therefore, means that the precise statements of the position and momentum of electrons have to be replaced by the statements of probability, that the electron has at a given position and momentum. This is what happens in the quantum mechanical model of atom.
= . × m s – (1J = kg m s – ) = . × m s – Problem . A golf ball has a mass of 40g, and a speed of m/s.
If the speed can be measured within accuracy of %, calculate the uncertainty in the position. The uncertainty in the speed is %, i.e., Using the equation ( . ) = . × – m This is nearly ~ times smaller than the diameter of a typical atomic nucleus.
As mentioned earlier for large particles, the uncertainty principle sets no meaningful limit to the precision of measurements. Reasons for the Failure of the Bohr Model One can now understand the reasons for the failure of the Bohr model. In Bohr model, an electron is regarded as a charged particle moving in well defined circular orbits about the nucleus. The wave character of the electron is not considered in Bohr model.
Further, an orbit is a clearly defined path and this path can completely be defined only if both the position and the velocity of the