Louis De Broglie (1924)

• French physics graduate student

• Proposed idea that accounted for the fixed energy levels in Bohr’s model

If waves can have particle like characteristics, then can

particles, such as electrons, have wave like characteristics???

What he knew…

• Electrons have wavelike motion (because it’s a particle)

• An electron had restricted orbits

• Each orbit had a fixed radius from the nucleus

• Are a wide variety of wavelengths, frequencies, and energies possible?

• No…there could only be allowed certain possible frequencies, wavelengths, and energies in an atom

• De Broglie came up with an equation for the wavelength of a particle of mass (m) moving at velocity (v).

De Broglie’s Equation

What does this equation do?

• What are we using?– Wavelength– Planck’s constant– Mass of the particle– Velocity

• Tells us that all moving particles have wave-like characteristics

Food for thought…

• Cars?• Baseball?• Do these have

wavelike characteristics? Why or why not?

Yes…let’s look at the equation…

λ= h mv

• The car and the baseball do have a velocity and a mass…• Using De Broglie’s equation we do get a wavelength for

the movement of a baseball and a car…• Let’s try the calculation…

Problem time…

• Mass of car= 910 kg• Velocity of car= 25m/s• What is the wavelength of the moving car?

– 2.9 x 10^-38 m

• How big is this?• Can we see or measure this wavelength?

– No, much to small to be detected, even with the most sophisticated equipment

Another one…

• Electron speed= 25 m/s

• Electron mass= 9.11 x 10^-28 g

• What is the wavelength of the moving electron?– 2.9 x 10^-5 m

• Do you think we can measure this wavelength and see it?– Yes, with the right equipment

Practice makes perfect

• What is the wavelength of an electron of mass 9.11 x 10-28 kg traveling at a velocity of 2.00 x 108 m/s? (Planck's constant = 6.63 x 10-34 J/Hz.

• 3.64 x 10-15m.