Themes > Science > Chemistry > General Chemistry > Atomic Structure > Electronic Structures of Atoms > Atomic Structure Index > Particle wave behavior

Early in the 20th century it was discovered that light, which everyone thought was a wave actually had particle like properties: it comes in discrete units called photons. In 1923, deBroglie completed the duality by showing that particles like electrons exhibit wavelike behavior: they have a wavelength and a frequency, just like light.

The wavelength of a particle turns out to depend on both its speed and the mass of the particle

l = h/m*v
where h is Planck's constant (6.626*10-34 J*s), m is the mass of the particle and v is the velocity of the particle. (Careful not to confuse v with the frequency n.) You need to be careful about the units: a J is a kg*m2/s2, so your mass must be in kilograms and your speed in meters/second.

Note that the wavelength is inversly proportional to the mass. This means the wavelength is very small for macroscopic objects like baseballs or people, and is why we don't notice wavelike behavior for large objects.

Example: What is the wavelength of an electron moving at 1/2 the speed of light (1.5*108 m/s). How about a 200 gram baseball moving at 50 m/s? (The speed of a good fastball.)

Solution: Simply use the equation above.

l = h/m*v
For the electron, the mass is 9.11*10-31 kg, so
lelectron = 6.626*10-34 J*s / (9.11*10-31 kg * 1.5*108 m/s)
lelectron = 4.8*10-12 m
For the baseball, the same relationship applies, but remember to convert the mass into kg from grams
lbaseball = 6.626*10-34 J*s / (0.200 kg* 50 m/s)
lbaseball = 6.6*10-35 m
Note that while the wavelength of the electron is on the order of the diameter of an atomic nucleus and thus measureable, there's no way we can ever measure the wavelength of a baseball.


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