7.2WaveNatureofMatter

# 7.2WaveNatureofMatter - Wave properties of matter 7.2 Wave...

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1 7.2 Wave Nature of Matter De Broglie Wavelength Diffraction of electrons Uncertainty Principle Wave Function Tunneling Wave properties of matter Material particles behave as waves with a wavelength given by the De Broglie wavelength (Planck’s constant/momentum) The particles are diffracted by passing through an aperture in a similar manner as light waves. The wave properties of particles mean that when you confine it in a very small space its momentum (and kinetic energy) must increase. (uncertainty principle) This is responsible for the size of the atom. Wave properties are only dominant in very small particles. h p λ = De Broglie Wavelength Momentum of a photon - inverse to wavelength. E p c = Einstein’s special relativity theory h p = λ since hc E = λ Wavelength of a particle- inverse to momentum. h p λ= Lois De Boglie De Broglie proposed that this wavelength applied to material particles as well as for photons. (1924) Wave properties a λ θ Diffraction of waves Increases as the ratio λ /a de Broglie wavelength of a baseball mv h p h = = λ A baseball with a mass of 0.15 kg is pitched at 45 m/s What is its De Broglie wavelength? m= 0.15 kg v= 45 m/s m 10 x 8 . 9 ) s / m 45 )( kg 15 . 0 ( 10 x 6 . 6 35 s . j 34 = = Diffraction effects of a baseball are negligible de Broglie wavelength of an electron meV 2 h p h = = λ eV m 2 p m 2 v m mv 2 1 KE 2 2 2 2 = = = = V = 1000 V + - e - Find the de Broglie wavelength of a 1000 eV electron.

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## This note was uploaded on 06/03/2010 for the course PHYS physics 1c taught by Professor Smith during the Spring '09 term at UCSD.

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7.2WaveNatureofMatter - Wave properties of matter 7.2 Wave...

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