The Dual Nature of the Electron

# The Dual Nature of the Electron - 6 m/s(the mass of the...

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The Dual Nature of the Electron Depending on the experimental circumstances, EM radiation appears to have either a wavelike or a particlelike (photon) character . Louis de Broglie (1892-1987) who was working on his Ph.D. degree at the time, made a daring hypothesis: if radiant energy could, under appropriate circumstances behave as though it were a stream of particles, then could matter, under appropriate circumstances, exhibit wave-like properties? For example, the electron in orbit around a nucleus . DeBroglie suggested that the electron could be thought of as a wave with a characteristic wavelength. He proposed that the wavelength of the electron was a function of its mass (m) and its velocity ( υ ): i.e. the wavelength for "matter waves", where h is Planck's constant and is υ velocity (not, the frequency). The quantity m υ for any object is its momentum (mass * velocity). What is the characteristic wavelength of an electron with a velocity of 5.97 x 10

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Unformatted text preview: 6 m/s? (the mass of the electron is 9.11 x 10-28 g) Planck's constant (h) is 6.63 x 10-34 J s (also, recall that 1J = 1 kg m 2 /s 2 ) converting g to kg: Converting from kg m 2 /s 2 to Joules: • The relationship between energy ( E ) and frequency ( ν ) for electromagnetic radiation (Planck's quantum of energy) • The relationship between wavelength ( λ ) and frequency ( ν ) for electromagnetic radiation From these relationships, we can determine the relationship between energy and wavelength: or, rearranging: • The relationship between wavelength ( λ ) and momentum (m*v) for DeBroglie's "particle wave" From the above relationships, we can calculate the relationship between energy ( E ) and momentum (m*v) Simplify, and solve for E : The highest velocity (v) attainable by matter is the speed of light ( c ), therefore, the maximum energy would seem to be: or...
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The Dual Nature of the Electron - 6 m/s(the mass of the...

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