The diffraction of radiation can be used to determine the spacing between atoms.

Question

The diffraction of radiation can be used to determine the spacing between atoms. In practice, the wavelength of the radiation used should be restricted to a value which is of the same order of magnitude as the interatomic distances to be determined. Such experiments are commonly performed using X-rays (electromagnetic radiation), however a beam of subatomic particles, such as of neutrons or electrons, may also be used if their corresponding de Broglie wavelength is of the appropriate magnitude.

Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one four thousandth of the speed of light (c/4000). (Enter at least 4 significant figures.)

h = 6.62608×10-34 J s c = 2.99792458×108 m/s Take care to distinguish "v", the symbol for velocity, from "nu" (the greek letter nu) -- which is the symbol used for frequency. Submit Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 111.5 pm. (1 pm = 10-12 m)

Explanation / Answer

debroglie wavelength, lambda = h/mv

a. m = 1.67493*10^-27 kg
v = c/4000
lambda = 6.62608*10^-34*4000/1.67493*10^-27*299792458 = 5.2783635 * 10^-12 m
b. v = h/m*lambda = 6.62608*10^-34/9.10939*10^-31*111.5*10^-12 = 6523677.925 m/s

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