^de – Broglie hypothesis

All material microscopic particle have dual nature, i.e. they can behave like particle as well as like a wave. Wavelength associated with a particle of momentum p is given

de Broglie waves are also known as Matter waves, pilot waves, stationary waves or probability waves. Theses are neither mechanical (as can be propagated even in vacuum) nor electromagnetic (as not produced by accelerated charges necessarily).

1.  For charged particles

Using values of h, m & q for an electron one can write:

For a 120 V accelerating potential, the above equation gives λ = 1.12 A⁰. This wavelength is of the same order as the spacing between the atomic planes in crystals.

In a similar way we can write

2.   For Neutral particles

(a) For neutron we need to put K & m.

^Electrons

J. J. Thomson was the first to determine experimentally the speed and the specific charge (e/m) of the cathode ray particles.  He found

1. cathode rays travel with speeds ranging from about 0.1 to 0.2 times the speed of light.
2. e/m = 1.76 × 10¹¹ C/kg.
3. the value of e/m is independent of the nature of the material/metal used as the cathode (emitter), or the gas introduced in the discharge tube. This observation suggested the universality of the cathode ray particles.

^Power of photons

Rate of energy of photons is called power of photons. If n photons each of wavelength ‘l’ are crossing a given area at right angles every second, then power of photons is defined as,

^Energy of photons

Max plank suggested that any source of radiation emits or absorbs energy discontinuously in the form of energy particles or packets of energy called photons. Amount of energy of an EM wave of frequency f possessed by a single photon is,

Total energy of EM wave having N photons is

E = Nhf.

Here h is Planck’s constant. It’s value is

h = 6.63 x 10^–34 Js = 4.14 x 10^–15 eVs

Dimensions of Planck’s constant & angular momentum are same & are [ML² T ^{– 1}].

^What are photons

Photons are electrically neutral energy particles of zero rest mass emitted by a source of radiation & travel along a straight line with a speed equal to speed of light. Zero rest mass implies that the photons can’t exist at rest. Photons travel in a straight line with a speed equal to speed of light. Being electrically neutral, photons are not deflected by electric and magnetic fields.