Lesson Notes By Weeks and Term - Senior Secondary School 2

Wave Particles Duality (Paradox)






TOPIC: Wave Particles Duality (Paradox)


Duality of Light

Duality of Matter

Uncertainty Principle.

The principle of wave-particle duality explains the dual nature of matter as a wave and as a particle.

Duality of Light

Light is an electromagnetic wave which radiates out from its source with a velocity of 3 x 108m/s. This can be use to explain the concepts of reflection, refraction and interference. To explain other concepts like emission, absorption, photo electric effect and radiation of energy by heated bodies, it is assumed that light energy travels through space in the form of concentrated bundles of energy called photons. Each photon is assumed to have energy E = hF. According to planck’s theory. H is called Planck constant. Thus, the particle nature of light is highlighted.


Briefly explain the duality of light.

Explain three concepts that shows the behaviour of light as particle.

Duality of Matter

Newton’s theories and laws considered matter and electrons as particles. De Broglie postulated that an electron mass ‘m’ moving with a velocity V radiates energy at a frequency f = �MV �and wavelength � � � = �h� ��( h = Planck constant ). This is true for electrons and�

�������H� � � � � � � � � � � � � � � � � � � � � Mv

Other elementary particles like protons and neutrons.


What is the energy of a photon whose frequency is 50KHZ, given that Planck constant, h= 6.6 x 10-34 Js.

A bullet of mass 0.002kg is fired with a velocity of 1000m/s. what is its de Broglie wavelength?� Will the wave nature of this mass be observable?


Heinsberg has shown by this experiment in electron diffraction that it is impossible to know the exact position and velocity of a particle at any given time. In the experiment, an electron was assumed to be a bundle of waves which extends over a small region � � � s.� The exact position of the atom in this bundle and within space� � � s is difficult to know. This uncertainty is called, the uncertainty of indeterminacy.

He therefore says that if� � s is the uncertainty in the position and � v the uncertainty in the velocity of a particle, � s� v >� ��h , m is the mass of the particle.�


If P is the� momentum, then � � � P =� � � � � MDV

:. ��� PDX > h ;� ��� E��� � � t > h

��� E is the uncertainty in the energy of the particle and� � t, the uncertainty in time. Hence, this principle is saying that we cannot determine the exact values of these quantities.


Explain Heinsberg uncertainty principle

State two phemomena that can be satisfactorily explained by assuming that matter behaves like�

��(a� ) waves��� (b) particles.


1.Which of the following are not� complimentary variables

  1. Energy and time � � � (b) energy and position � � (c ) Energy and mass� (d) Velocity and position .
  2. Which of the following factors does not support the wave model of light?

(a) Diffraction��� ��� (b) Interference � � � (c )Refraction� � (d) Photo emission

  1. According to quantum theory, electromagnetic wave is transmitted in tiny bundles of energy called

(a) phonons��� ��� ��� (b) electrons��� ��� (c ) photons� � � � (d) protons

  1. Which of the following scientists proposed the uncertainty principle?

(a) De Broglie��� ��� (b) Heinsberg��� ��� (c) Newton� � � � � � � � (d)Lenz


  1. With what fundamental accuracy can the position of a 60g piece of stone be located, if the stone has a speed of 240m/s, accurate to 0.1%.
  1. Explain what is meant by the duality of matter, illustrating your answer with observable phenomenon.

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