Title 12. ATOMS.pdf ✅

Atoms r n m h e n =             2 2 0 2 2 4 π πε For innermost orbit n = 1; the value of r1 is known as Bohr’s radius a0. a h me 0 2 0 2 = ε π If we put values of all constants, we get a0 = 5.29×10–11 m » 0.53 Å It can also be observed that radius of nth orbit increases by n2 times. By putting this value in total energy of an electron and convert the unit in eV, we get E n n = −13 6 2 . eV Negative value shows that electron is bound to nucleus. Limitation of Bohr’s atomic model:  Bohr’s model is for hydrogenic atoms. It does not hold true for a multi-electron model. KEY FORMULAE Radius of orbit, r e mv = 2 2 4πε0 Kinetic energy of electron in its orbit, K e r = 2 0 8πε PE of an electron, U e r = 1 4 0 2 − πε . Velocity of electron in its orbit, v e mr = 4πε0 Spectral series Lyman Series: 1 = 1 1 1 ; 2 2 λ R n −       n = 2, 3, 4, 5, ....This is in UV range. Balmer Series: 1 = 1 2 1 2 2 λ R n −      , n = 3, 4, 5..... This is in visible range. Paschen Series: 1 1 3 1 ; 2 2 λ = −       R n n = 4, 5, 6 ..... Brackett Series: 1 1 4 1 ; 2 2 λ = −       R n n = 5, 6, 7... Pfund Series: 1 1 5 1 ; 2 2 λ = −       R n n = 6, 7, 8....          These series are in infrared region. Relation between speed, total energy of an electron and its radius with respect to orbital number n: v n e h n = 1 1 2 2 0 4πε π ( / ) r n m h e n =               2 0 2 2 4 π πε 2 Bohr radius, a h me 0 2 0 2 = = 0.53A ° ε π Energy for nth orbiting electron, E n n = −13.6 eV 2 Total energy of an electron in an orbit, E e r = − 2 0 8πε MNEMONICS P fund series. n =5 1 Papa brings Pastry for Ba ub and Lal Concept: Hydrogen Spectra: Mnemonics: Interpretation: Paschen series. n =3 1 Balmer series. n =2 1 Lymans series. n =1 1 Brackett series. n =4 1