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  • Einstein has suggested that light can behave as a wave as well as like a particle i.e, it has dual character. In 1924, de-Broglie suggested that just as light exhibits wave and particle properties, all microscopic material particles such as electrons, protons , atoms, molecules, etc. also have dual character. They behave as a particle as well as a wave. This means that an electron which has been regarded as a particle also behaves like a wave. Thus, according to de-Broglie,

    all the material particles in motion possess wave characteristics.

    According to de-Broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation,
    $$\lambda=\frac{h}{mv}=\frac{h}{p}$$
    where h is Planck's constant, v is the velocity and p(=mv) is momentum of the particles. The waves associated with material pariticles are called de Broglie waves.

  • My book says that:

    "Although the dual nature of matter is applicable to all material objects but it is significant for microscopic bodies only. For large bodies, the wavelengths of the associated waves are very small and cannot be measured by any of the available methods. Therefore, practically these bodies are said to have no wavelengths. Thus, any material body in motion can have wavelength but it is measurable or significant only for microscopic bodies such as electron, proton, atom or molecule. This may be illustrated as follows:
    The wavelength of an electron with mass $9.11*10^{-31}$kg and moving with the velocity of $10^6$ m/s is $7.28$ m as shown below:
    $$\lambda=\frac{h}{mv}=\frac{6.63*10^{-34}kg m^2 s^{-1}}{(9.11*10^{-31}kg)(10^6m/s)}=7.28*10^{-10}m$$
    This wavelength associated with the moving electron is of the same order of magnitude as of $X$-rays which can be easily measured."

  • I made an attempt to check the wavelength associated with a car of mass $10^{6}$ kg and moving with velocity of $9.11*10^{-31}$ m/s, and I got the wavelength associated with it as shown below:
    $$\lambda=\frac{h}{mv}=\frac{6.63*10^{-34}kg m^2 s^{-1}}{(10^6kg)(9.11*10^{-31}m/s)}=7.28*10^{-10}m$$
    This shows that a car or any material object with mass $10^{6}$kg and moving with velocity $9.11*10^{-31}$m/s (almost at rest) has the wavelength same as that of an electron, but this result in contradiction with the statement of my book. And even I thought that it is practically impossible to see any wavelength associated with such mass of $10^{6}$kg.

I have heard about rest and relativistic mass, and theory of relativity, but I have naive idea about it. If I have made mistake there, correct me. Or else "is it that macroscopic body can have same wavelength as that associated with an electron?" Please explain.

Sensebe
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1 Answers1

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The generic textbook explanation why we do not see quantum effects in the macroscopic world is decoherence.

However, there's an even simpler explanation for your particular example: The de Broglie wavelength is far smaller than the size of your macroscopic object, so good luck trying to squeeze your car through the gaps between the atoms in a crystal lattice you use for X-ray diffraction ;)

As in, it's not so much the absolute size of the wavelength that matters, but rather its relative size.

Christoph
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    Right for practical purposes, though in principle decoherence is indeed the more relevant aspect. At sufficiently low temperatures, the wave-behaviour of e.g. buckyballs can very much be relevant even if the wavelength is smaller than the molecules themselves. – leftaroundabout Jan 05 '14 at 13:06