**CBSE NOTES CLASS 12 PHYSICS **

**CHAPTER 11 DUAL NATURE OF RADIATION AND MATTER**

**Wave nature of matter**

The wave nature of light shows up in the phenomena of interference, diffraction and polarisation. On the other hand, in photoelectric effect and Compton effect which involve energy and momentum transfer, radiation behaves as if it is made up of a bunch of particles – the photons.

The gathering and focusing mechanism of light by the eye-lens is understood in the wave picture.

But its absorption by the rods and cones (of the retina) requires the photon picture of light.

Louis Victor de Broglie suggested that moving particles of matter should display wave-like properties under suitable conditions. He reasoned that nature was symmetrical and that the two basic physical entities – matter and energy, must have symmetrical character. If radiation shows dual aspects, so should matter.

De Broglie proposed that the wave length λ associated with a particle of momentum p is given as

$$\mathrm{\lambda}\mathrm{}=\frac{\mathrm{h}}{\mathrm{p}}=\mathrm{}\frac{\mathrm{h}}{\mathrm{m}\mathrm{v}}$$

where m is the mass of the particle and v its speed.

Now if V is the magnitude of accelerating potential in volts,

K = eV

$$\mathrm{B}\mathrm{u}\mathrm{t}\mathrm{}\mathrm{}\mathrm{K}\mathrm{}\mathrm{}=\frac{1}{2}\mathrm{}\mathrm{m}{\mathrm{v}}^{2}=\frac{{\mathrm{p}}^{2}}{2\mathrm{m}}$$

$$\Rightarrow \mathrm{}\mathrm{p}=\sqrt{2\mathrm{m}\mathrm{K}}=\sqrt{2\mathrm{m}\mathrm{}\mathrm{e}\mathrm{V}}\mathrm{}$$

$$\Rightarrow \mathrm{\lambda}\mathrm{}\mathrm{}=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}\mathrm{K}}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}\mathrm{}\mathrm{e}\mathrm{V}}}=\frac{1.227}{\sqrt{\mathrm{V}}}\mathrm{}\mathrm{n}\mathrm{m}$$