3.9 Sspd_chapter1_part6_neil bohr's quantum theory of atoms.

SSPD_Chapter 1_Part 6_NEIL BOHR’s QUANTUM THEORY OF ATOMS- STATIONARY AND RADIATION LESS ORBITS.

According to Classical Physics any accelerated charge will radiate electromagnetic waves called Synchrotron Radiation .

Electrons in circular orbits around the nucleus experience a centripetal force due to electrostatic attraction ((q.q)/(4πε _o r ² )) and a reaction force called centrifugal force equal to mv ² /r. An exact balance between the two keeps it in a stable circular orbit. If energy is being lost through radiation , due to the fact that a particle in a circular orbit is being continuously accelerated towards the centre, then the orbiting electron will spiral inward until it collapses into the nucleus. But no such thing happens in reality in an Atom though we do witness the phenomena of Synchrotron Radiation in a Betatron.

As shown in Fig.(1.11) , Betatron consists of a powerful magnetic field along z axis perpendicular to the plane of paper. The electron is accelerated along an expanding spiral path in the plane of the paper around the longitudinal axis of the magnetic field. An electric field is applied parallel to the plane of paper by two oppositely charged D shaped electrodes which accelerate the electron every time it passes from one electrode region to the other region. The electric field is alternating field with period of alteration equal to the time taken to cover one circular path. This keeps accelerating electron into expanding spiral path.

Fig.1.11. The schematic of a Betatron

The outward spiraling electron radiates a continuous spectrum of soft X-ray electromagnetic waves. This finds several commercial applications in the field of medicine and industries.

But what is true at macro scale is not true at the atomic scale. Why?

In 1913 Niels Henrik David Bohr(1885-1962) [Appendix XXIV] proposed a new set of postulates to circumvent this difficulty:

1. Electrons are permitted only in those orbits which are radiation less and support standing waves of electron probability amplitude Ψ(r,t);

(ii) Electron Orbital Angular Momentum= integral multiple of (h/(2π));

i.e. Iω = nћ 1.15

where I =moment of inertia around the spin axis= mr ² ;

and ω= orbital angular velocity = v/r;

1. A photon is emitted when electron jumps from excited state to ground state. A photon is absorbed when electron jumps from ground to a excited state. In both the cases, that is in the case of radiation or absorption, the photon’s energy packet hν = ΔE = E ₂ (excited state) – E ₁ (ground state);

Neil Bohr himself did not prove these postulates. Heisenberg used Quantum Mechanics to prove these postulates and Schrödinger used Matrix Mechanics to prove the same. Heisenberg was awarded Nobel Prize in 1932 for his contribution to Quantum Mechanics.

According to Matter Wave Theory, an electron in free space has a continuum of energy. It behaves as a traveling wave and its wave number and orientation can be continuously varied. This electron can occupy any energy level from zero to infinity.