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# Wave – Particles Duality (Paradox)

CONTENT

• 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.

EVALUATION

1. Briefly explain the duality of light.
2. Explain three concepts that show the behavior of light as particle.

DUALITY OF MATTER

Newton’s theories and laws considered matter and electrons as particles. De Broglie postulated that an electron of mass ‘m’ moving with a velocity v radiates energy and has a wavelength, ʎ =  h  /mv  (h = Planck constant).

This is true for electrons and other elementary particles like protons and neutrons.

EVALUATION

1. What is the energy of a photon whose frequency is 50KHz, given that Planck constant, h= 6.6 x 10-34 Js.
2. 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?

UNCERTAINTY PRINCIPLE

GENERAL EVALUATION

1. Explain Heisenberg uncertainty principle
2. State two phenomena that can be satisfactorily explained by assuming that matter behaves like (a) waves (b) particles.

WEEKEND ASSIGNMENT

1.   Which of the following are not complimentary variables (a) Energy and time (b) energy and position     (c) Energy and mass  (d) Velocity and position .

2.   The duality of matter implies that matter? (a) Exist as particle of dual  composition (b) has momentum and energy (c) has both wave and particle property (d) is made up of dual materials

3.   According to quantum theory, electromagnetic wave is transmitted in tiny bundles of energy called (a) photons (b) electrons (c) photons (d) protons

4.   Which of the following scientists proposed the uncertainty principle? (a) De Broglie

(b) Heisenberg (c) Newton (d) Lenz

5.   The uncertainty in the measurement of two complementary variables is ____ (a) ≥ (b) ≥ (c) ≈ (d) =

THEORY

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%.

2.   (a) State Heisenberg uncertain principle.

(b) Mention two phenomena that can be explained in terms of the particulate nature of light.