Kinetic energy of electron in any orbit is given by E k = 2π 2 me 4 Z 2 K 2 / n 2 h 2 = 13.6 Z 2 / n 2 eV Potential energy of electron in any orbit is given by
E p = – 4π 2 me 4 Z 2 K 2 / n 2 h 2 = 27.2 Z 2 / n 2 eV
⇒ E p = ∝ Z 2 / n 2
Total energy of electron in any orbit is given by
E = – 2π 2 me 4 Z 2 K 2 / n 2 h 2 = – 13.6 Z 2 / n 2 eV
⇒ Ep = ∝ Z 2 / n 2
Wavelength of radiation emitted in the radiation from orbit n 2 to n 1 is given by
In quantum mechanics , the energies of a system are discrete or quantized . The energy of a particle of mass m is confined to a box of length L can have discrete values of energy given by the relation
E n = n 2 h 2 / 8mL 2 ; n < 1 , 2 , 3 ,…
Hydrogen Spectrum Series
Each element emits a spectrum of radiation , which is characteristic of the element itself . The spectrum consists of a set of isolated parallel lines and is called the line spectrum .
Hydrogen spectrum contains five series
( i ) Lyman Series When electron jumps from n = 2 , 3,4 , … orbit to n = 1 orbit , then a line of Lyman series is obtained .
This series lies in ultra violet region .