 # Dual nature of matter and De-Broglie's relationship

De - Broglie's wave theory Vs Bohr atomic model :

2\pi r = n\lambda
n = integral value
2\pi r = n\frac{h}{mv}
mvr = \frac{nh}{2\pi}

### View the Topic in this Video from 42:00 to 51:00

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1. de-Broglie equation, \tt \lambda=\frac{h}{p}=\frac{h}{mv}=\frac{h}{\sqrt{2mE_{k}}}=\frac{h}{\sqrt{2mqv}}

2.Planck's Equation, \tt E=h\nu=\frac{h.c}{\lambda}

3.Einstein's mass energy relationship, E = mc2

4.de Broglie wavelength associated with charged particles

(a) For electron \tt \lambda = \frac{12.27}{\sqrt{V}}Å
(b) For proton \tt \lambda = \frac{0.286}{\sqrt{V}}Å
(c) For α -particles \tt \lambda = \frac{0.101}{\sqrt{V}}Å
where V is the accelerating potential of these particles.

5.de Broglie wavelength associated with uncharged particles
(a) For neutrons
\tt\lambda=\frac{h}{\sqrt{2Em}}=\frac{6.62\times10^{-34}}{\sqrt{2\times1.67\times 10^{-27}\times E}}=\frac{0.286}{\sqrt{E\left(eV\right)}}Å

(b) For gas molecules \tt\lambda=\frac{h}{m\times u_{rms}}=\frac{h}{\sqrt{3mkT}}
where k is the Boltzmann constant.