How to Calculate de Broglie Wavelengths

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In 1923, Louis de Broglie proposed that because light can behave as particles even though it possesses no mass, objects with mass can also exhibit wave-like properties. De Broglie merged equations for the energy of a particle with mass and the energy of a light particle with no mass and arrived at the equation lamba = h / mv, where lambda represents the wavelength in meters, h is Planck’s constant (6.626 x 10^-34 joule seconds), m represents the object’s mass in kilograms and v represents its velocity in meters per second. Thus, any object with mass that exhibits motion will also exhibit a de Broglie wavelength.

Things You'll Need

  • Scientific calculator
  • Determine the mass of the object under investigation in units of kilograms. If you are working with a problem from a textbook, this information may be provided directly. Otherwise, place the object on a balance or scale and determine its mass. If your balance or scale does not measure in kilograms, then use an online tool to convert its units to kilograms. For example, consider an 8-pound bowling ball, which converts to 3.6 kilograms.

  • Calculate or otherwise determine the object’s velocity in units of meters per second. Velocity represents distance traveled divided by elapsed time. For example, the length of a bowling alley is 60 feet from the foul line to the first pin, which converts to 18.3 meters. If the bowling ball requires 4.6 seconds from time of release until it strikes the pins, then it exhibits an average velocity, v, of v = 18.3 meters / 3.9 seconds = 4.7 meters per second.

  • Determine the de Broglie wavelength according to lambda = h / mv. Continuing with the previous example, lambda = (6.626 x 10^-34) / (3.6 * 4.7) = 3.9 x 10^-35 meters.

Tips & Warnings

  • Numbers such as 6.626 x 10^-34 represent scientific notation, which scientists commonly use to express very large or very small numbers. The “x 10^-34” means “times ten to the negative thirty-fourth power.” Scientific calculators allow you to enter these numbers directly with scientific notation function, which is typically abbreviated “EE.” The proper keystrokes would therefore be [6] [.] [6] [2] [6] [EE] [-] [3] [4].

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