The Dual Nature of the Electron

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 ( ) for electromagnetic radiation (Planck's quantum of energy) The relationship between wavelength ( ) and frequency ( ) for electromagnetic radiation From these relationships, we can determine the relationship between energy and wavelength: or, rearranging: The relationship between wavelength ( ) 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...
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online