After the work of Planck, Einstein and Compton it was established that radiation has dual nature. It acts like a wave in some situations and as a particle in some other situations.

E=hν

p = E/c = h ν/ c

p = h/λ

λ = h/p

λ = h/mv

This is called de Broglie’s Hypothesis and is called de Broglie wavelength, the associated wave is called matter wave or de Broglie wave.

2 π r = n λ → 1

mvr = nh/2 π→ 2

n λ = 2 π (nh/2 π mv)

λ = h/mv

De Broglie wave for n=5 Bohr orbit

p = h/ λ = ħk

E = ħω

p = ħk

Basic relations of Quantum theory

Expression for De Broglie Wavelength:

For Nonrelativistic case:

• In terms of Kinetic Energy:

• In terms of Accelerating potential:

For Relativistic case:

• In terms of Kinetic Energy:

• In terms of Accelerating Potential: