Application to the Bohr model

De Broglie expanded the Bohr model of the atom by showing that an electron

es48 in orbit around a nucleus could be thought of as having wave-like properties. In particular, an electron will be observed only

ewm1000 in situations that permit a standing wave around a nucleus. An example of a standing wave is a violin string, which is fixed at both ends and can

fan7530 be made to vibrate. The waves created by a stringed instrument appear to oscillate in place, moving from crest to trough in an up-and-down motion. The wavelength of a standing

fc114 wave is related to the length of the vibrating object and the boundary conditions. For example, because the violin string is fixed at both ends, it can carry standing waves of wavelengths 2l/n, where l is the

fc-255 length and n is a positive integer. De Broglie suggested that the allowed electron orbits were those for which the circumference of the orbit would be an integer number of wavelengths.