Wave Nature Of Matter And De Broglie's Equation - Practice Questions & MCQ

As we know light behaves both as a wave and particle. Because If you are observing phenomenon like the interference, diffraction or reflection, you will find that light is a wave. However, if you are looking at phenomena like the photoelectric effect, you will find that light has a particle character.

De Broglie’s hypothesis stated that there is symmetry in nature and that if the light behaves as both particles and waves, matter too will have both the particle and wave nature.

i.e if lightwave can behave as a particle then the particle can also behave as waves.

De Broglie’s Equation-

According to De Broglie, A moving material particle can be associated with the wave.

De Broglie proposed that the wavelength  associated with the moving material particle of momentum p is given as 

where  and 

further, we can write De - Broglie wavelength as

where 

So from De Broglie’s Equation, we can conclude that-

i.e Wavelength associated with a heavier particle is smaller than that with a lighter particle.

i.e when Particle moves faster, then wavelength will be smaller and vice versa

• if the particle at rest then De - Broglie wavelength will be infinite ()
• 
• De - Broglie wavelength (λ) is independent of charge. 

De - Broglie wavelength of Electron-

As De Broglie’s Equation is given as 

So for an electron having velocity v attained by it when it is accelerated through a potential difference of V.

then (Kinetic energy gain by the electron)=(work is done on an electron by the electric field)

i.e 

So De - Broglie wavelength of Electron is given as 

using  and  and 

we get     ( i.e answer will be in ) 

Similarly, we can find De - Broglie wavelength associated with charged particle

De - Broglie wavelength with charged particle-

Where 

• De - Broglie wavelength of the proton

     using  and 

we get 

• De - Broglie wavelength of Deuteron

using  and 

we get 

•  De - Broglie wavelength of an Alpha particle  (He²⁺⁾

using  and 

we get 

• Electron microscope-

An electron microscope is an important application of de-Broglie waves designed to study very minute objects like viruses,
microbes and the crystal structure of the solids. In the electron microscope, by selecting a suitable value of potential difference V ,we can have an electron beam of as small wavelength as desired. And this de-Broglie wavelength is calculated by using the formula .