Structure of Atom
8.0 Dual Behaviour of Matter
8.0 Dual Behaviour of Matter
- De Broglie proposed that like radiation, matters should also exhibit dual behaviour i.e particle like andwave like.
- De Broglie gave a relation between wavelength $(\lambda) $ and momentum(p) of a material particle
$$\lambda = \frac{h}{p} = \frac{h}{{mv}}$$
where m is the mass of the particle, v is the velocity and p is its momentum.
- Experimentally it was found that an electron just like waves, undergoes diffraction.
- Other formulae is
$$\lambda = \frac{h}{{\sqrt{2mKE}}}$$
where KE is Kinetic Energy of particle
- If a Charged Particle is accelerated by V Volt initially from rest then
$$\lambda = \frac{h}{{\sqrt{2mqV}}}$$
- For an electron; q=e, m= $9.1 \times {10^{-31}}kg$
$$\lambda = {{12.27} \over {\sqrt V }}\mathop A\limits^ \circ $$
Example
Calculate the de Broglie wavelength associated with a cricket ball weighing 380 g thrown at a speed of 140 km per hour.
Solution:
Mass of the cricket ball = 380 g = $380 \times {10^{ - 3}}$ kg = 0.38 kg
Speed or Velocity = 140 km/hr = $140 \times \frac{{1000}}{{3600}}$ = $38.89$ $m{s^{ - 1}}$
The wavelength associated with the cricket ball will be
$\lambda = \frac{h}{{mv}} = \frac{{6.626 \times {{10}^{ - 34}}}}{{(0.38)(38.89)}}$
$ = 4.48 \times {10^{ - 35}}$$m$
