Question

state de broglie hypothesis with suitable equation​

Answer 1

DeBroglie Hypothesis

• DeBroglie stated that like matter,light shows dual nature too

• Light behaves both as a wave and a particle

Wave Nature

• Light is typically a electromagnetic wave which can be perceived by the human eye

• True to its wave Nature,light exhibits both diffraction and interference

• Like the UV Rays,Infra Red Rays etc

Particle Nature

• It is hypothesised that fundamental particles called Photons constitute light

• As a result,it shows photoelectric effect and scintillating

• Photons are small packets of energy

DeBroglie's Relation

According to Theory of Relativity,

$\sf{e = m {c}^{2} - - - - - - (1)}$

• Energy of the particle
• c is speed of light
• m is mass of the particle

Also,

$\sf{e = h \nu}$

But,

$\sf{ \nu = \dfrac{c}{ \lambda} }$

Implies,

$\sf{e = \dfrac{h}{ \lambda} \times c - - - - - (2) }$

• h is Planck's constant
• $\lambda$ is wavelength

Equating (1) and (2),we write :

$\large{ \sf{m { \cancel{c}^{2}} = \dfrac{h}{ \lambda} \times \cancel{c }}} \\ \\ \large{ \longmapsto \: \boxed{ \boxed{\sf{ \lambda \: = \dfrac{h}{mc} }}}}$

The following relation can be generalized for all particles by replacing the speed of light with a common notation of velocity

$\large{ \longmapsto \: \boxed{ \boxed{\sf{ \lambda = \dfrac{h}{mv} }}}}$

Answer 2

$\star{\bf{\underline{Answer:}}}$

Deriving the de Broglie Equation

The equation is E = h*nu, where e is energy, h is the Planck constant, and nu is frequency of the wave. Now, Planck's constant is a proportionality constant to describe the relation between the energy and the frequency.