CONCEPT OF BOHR'SRadius By-N.K.D. Sir Please -Rate review and share this lesson

Calculation of Bohr radius: The radius of the first orbit of hydrogen atom and like ions is called Bohr radius. mv/r (Centrifugal Force) E mass m Coulombic Force of Attraction Ze Nucleus Let us consider an electron of mass 'm'and charge 'e'moving round a nucleus of charge Ze, where Z is the atomic number and 'e is the charge on proton. Suppose v is the tangential velocity of electron in a orbit of radius '. By Coulomb's law, the electrostatic force of attraction (Fe) between the positively charged nucleus and electron is given by:

where 'k'is a constant and r is the radius of the orbit. Value of 'k'is given by, c is the permittivity of free space or air In C.G.S. units value of k is equal to 1. The centrifugal force (Fc) acting on the electron is given by, mv If the electron has to remain in the same orbit then mv

According to Bohr's postulate, nh mvr =- 2T For evaluating we have to remove v'between (3) and (4). So, on squaring expression 4 On substituting the value of mv2 from (3) into (5) 2 Ze my2

m n h n h ro From equation (7), we can calculate the radii of various orbits of hydrogen atom for which Z-1. Thus, for Hydrogen atom nh Now, radius of the first orbit (n-1) 4Tt me

On substituting the value of h 6.62x107 erg sec, ri Bohr radius (6.62x1027)2 4 x (3.14)2x9.1x1028 x (4.8x101 -0.529 x 10-8 cm Therefore, the radius of the nth orbit for hydrogen atom can be written as, Radius of the second orbit (n 2) i.e., radius of second orbit is four times of that first orbit. 0.529 Rm 0.529% n r2 0.529 x 22 -4 x 0.529 A The ratio of radius of hydrogen atom (protium), deuterium and tritium is 1: 1 1, because Z-1

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Niranjay Kumar Dwivedi

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Mukesh pandey

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9/ten ... thanks..it was short and crisp..

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