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An electron emitted in the beta decay of bismuth-210 has a mean kinetic energy of 390 keV. (a)...

Question:

An electron emitted in the beta decay of bismuth-210 has a mean kinetic energy of 390 keV.

(a) Find the de Broglie wavelength of the electron.

(b) Would such an electron be useful in a Davisson-Germer type scattering experiment?

The De-Broglie Wave

Inspired by Einstein's explanation of the photo-electric effect wherein it was suggested that radiation has a dual nature, Louis de Broglie suggested that matter too should exhibit the same kind of duality. In particular, microparticles have the right kind of momentum to exhibit wavelike behavior under suitable conditions. Thus when electrons of the right energy are allowed to impinge on a crystal then diffraction effects are expected just as in the case of X-rays. Such an experiment was done by Davisson and Germer with a nickel crystal and an electron beam of energy in the range of about 50 eV. The results were in striking conformity with the matter-wave hypothesis.

Answer and Explanation: 1

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The De-Broglie wavelength of a matter particle of momentum {eq}\displaystyle {p} {/eq} is given by,

{eq}\displaystyle...

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Wave-Particle Duality & the Davisson-Germer Experiment

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Chapter 23 / Lesson 2
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Wave-particle duality means that light and sub-atomic particles can also behave as waves, hence the duality. Study the definition of wave-particle duality, the Davisson-Germer Experiment, the de Broglie wavelength, and an example calculation.


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