CBSE Class 11-science Answered

Introduction to Heisenberg's Uncertainty Principle

 Electron is an extremely small micro particle moving with a very high velocity. Therefore , to locate the exact position of an electron in an atom we need a very sensitive instrument . We have to focus light on the electron and observe the reflect beam of light . For reflection to occur , the wavelength of the incident radiation must be smaller than the dimension of the object reflecting it . Radiations whose wavelengths are shorter than the size of an electron consist of high energy photons . During collision with such a high energy photon , the electron gets deflected as it absorbs considerable amount of energy resulting in the considerable increase in its momentum . This automatically changes the position of the electron . This inability is not due to lack of proper instruments but due to the limitations imposed by nature on such measurements . There is an inherent uncertainty in simultaneous determination of the position velocity of an electron . Summing up these facts , Heisenberg proposed the " Uncertainty principle"

Statement

" Simultaneous and exact determination of the position and momentum of a sub atomic particle like electron moving with high speed is impossible .

 Heisenberg's uncertainty principle is one of the basic principles of wave mechanics and has to be taken note of while dealing with small particles in motion . If the uncertainty in the determination of the position of a small particle is given by  Δx and the uncertainty in its momentum is Δp then ,

                                       (Δ x)  ( Δp)  >   h/n∏     ( where n = 1,2,3,4,........)

   At any particular instant , we need to know the distance of electron from the nucleus as well as its momentum . For an electron revolving round the nucleus in an atom the value of n is nearly 4 . Hence we can write

                                    (Δ x)  ( Δp)  >   h/4∏

 Thus Heisenberg's uncertainty principle can be stated as

     The product of uncertainty in position and that in momentum of a micro particle moving high speed cannot be less than  h/4∏.

why does electron cannot reside in the nucleus?

On the basis of Heisenberg's uncertainty principle, it can be shown as to why electron cannot exist within the atomic nucleus. The radius of the atomic nucleus is of the order of 10^-15 m. Now, if the electron were to exist within the nucleus, then the maximum uncertainty in its position would have been 10^-15 m.

Mass of electron, m = 9.1 x 10^-31 kg, Dx =1 x 10^-15 m.

The value of uncertainty in velocity, Dv is much higher than the velocity of light (3.0 x 10⁸ ms^-1) and therefore, it is not possible. Hence an electron cannot be found within the atomic nucleus.

or

electron cannot reside in the nucleus because the thing is that atomic nucleus or we can say that the atomic radius of the electron is bigger than the atomic radius of the nucleus itself. like a bigger thing can not fit into a smaller area like wise is the case with electrons