CONCEPT OF Velocity & energy of electrons in nth orbit (Bohrs atomic model) By-N.K.D. Sir Please -Rate review and share this lesson
Velocity of the electron in an orbit We know that the centrifugal force on the revolving electron is balanced by the attraction between the nucleus and the electron. mv2 Ze2 from equation (3)] or mv2r - e2 (when Z- 1, for hydrogen) mvr - " from equation (4) and Dividing equation (9) by (4), we get 2Tte (10) On substituting values of , e and h in the above equation, the velocity of electron in the nth stationary state is 2.19x10 cm sec-1 1l
Velocity of electron in the first orbit, ie. for n 1 (Bohr velocity) is given by V1 = 2.19 108 cm sec-1 Velocity of electron in first Bohr orbit is of velocity oflight. In the second orbit, velocity of electron will be half of its velocity in the first orbit, 137 2.19x108 So Number of revolutions per second made by an electron round the nucleus is given by Velocity of electron Circumference of of orbit
Energy of electron in different stationary states (orbits) The total energy of a revolving electron in any orbit is the sum of its kinetic and potential energies Total energy (E) = K. E. + P. E. Kinetic energy of an electron, K. E. =-mv2. From equation (9) we knowez 2 e e Z mv2 2 vor or 2r or . .- e2z 2r
The potential energy of an electron at a distance 'r' from the nucleus is given by the work done in bringing a unit charge from infinity to distance 'r' from the nucleus, which is equal to: Potential energy = Total energy (E, ) =-+-- 2r 2r n h On substituting the value of m2m valued'-law ]inthisrelation,weget, g 22in this relation, we get,
So, energy of electron in nth orbit is Il n h Substituting the values of , m, ez-1 and h, energy of an electron in the nth orbit is 2.179x10-1 2 erg/atom 13.6 2eV/atom 1eV 1.602 x 10-12 erg,) For hydrogen atom like ions, 13.6 Z2 2 eV/atom where Z is atomic number of the species.
The minus sign for the energy of an electron in an orbit represents attraction between the +vely charged nucleus and -vely charged electron. Energy of an electron at infinite distance from the nucleus is zero 3 As an electron approaches the nucleus, the electrical attraction increases, energy of electron * Energy of an electron increases as the value of"n, increases i.e., Enx or-En 3 Value of 'n' remaining unchanged, the amount of energy associated with an electron remains > Energy of electron in first, second, third and fourth orbit are -13.6, -3.4, 1.5, and -0.85 decreases and it becomes negative. unaltered eV/atom respectively Although the energy of electron increases with increase in the value of 'n' (orbit), yet the difference of energy between successive orbits decreases. Thus E2-E> E E> E4 E > Es - E4, etc....
Niranjay Kumar Dwivedi
(N.K.D.Sir) is a Complete Chemistry faculty for IIT~JEE, and NEET examination. with more then 8 year of Teaching experience