Quantum Physics Lesson 6 Wave Particle Duality Quantum Physics Lesson 6

Today’s Objectives Explain what is meant by wave-particle duality. Describe the main points of de Broglie’s hypothesis that matter particles also have a wave-like nature. State and use the equation λ = h/p = h/mv Describe evidence for de Broglie’s hypothesis.

Wave particle duality We have seen…………….. Photons : Quanta (particles) of light Electrons: Being diffracted. A property of waves

Prince Louis de Broglie 1892-1987 Electrons should not be considered simply as particles, but that frequency must be assigned to them also. (1929, Nobel Prize Speech)

De Broglie (1924) Suggested that particles such as electrons might show wave properties. He summised that the de Broglie wavelength, λ was given by: m = mass v = velocity of the particle

Note that:- This is a matter wave equation not electromagnetic wave The de Broglie wavelength can be altered by changing the velocity of the particle.

In words...

The diffraction tube

Summary of Experiment Beam of electrons directed at a thin metal foil. Rows of atoms cause the electron beam to be diffracted in certain directions only. We observe rings due to electrons being diffracted by the same amount from grains of different orientations, at the same angle to the incident beam.

What we should see

Electron diffraction 1927: Davisson & Gerner confirmed this prediction with experiments using electron beams. They actually used a nickel target instead of a carbon one (we used) The wavelength they measured agreed with de Broglie There is a relationship between the accelerating voltage V and the k.e. of the particles

Diffraction effects have been shown for Hydrogen atoms Helium atoms Neutrons Neutron diffraction is an excellent way of studying crystal structures.

Prince Louis de Broglie - 1932 DE BROGLIE WAVELENGTH Prince Louis de Broglie - 1932 De Broglie discovered that all particles with momentum have an associated wavelength. What is the wavelength of a human being, assuming he/she weighs 70 kg, and is running at 25 m/s?

1. Find the wavelength of an electron of mass 9 1.Find the wavelength of an electron of mass 9.00 x 10-31 kg moving at 3.00 x 107 m s-1 2.  Find the wavelength of a cricket ball of mass 0.15 kg moving at 30 m s-1. 3.  It is also desirable to be able to calculate the wavelength associated with an electron when the accelerating voltage is known. There are 3 steps in the calculation. Calculate the wavelength of an electron accelerated through a potential difference of 10 kV.

p = √2mEk = √2 x 9.1 x 10-31 x 1.6 x 10-15 = 5.4 x 10-23 kg m s-1 Step 1: Kinetic energy Ek = eV = 1.6 x 10-19 x 10000 = 1.6 x 10-15 J Step 2: EK = ½ mv2 = ½m (mv) 2 = p2 / 2m, so momentum p = √2mEk = √2 x 9.1 x 10-31 x 1.6 x 10-15 = 5.4 x 10-23 kg m s-1 Step 3: Wavelength l = h / p = 6.63 x 10-34 / 5.4 x 10-23 = 1.2 x 10-11 m = 0.012 nm.

Laser d2 d1 L1 Slits L2 Screen 1 Screen 2 Slit spacing, d Wavelength,  Distance to screen, L Fringe spacing, x Laser d2 d1 L1 Slits L2 Screen 1 Screen 2

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