Question

why de broglie relationship is not applicable for large bodies
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Answer 1

Answer:

According to de-Broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by the relation,

λ=hmv=hp

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∗10−31kg and moving with the velocity of 106 m/s is 7.28 m as shown below:

λ=hmv=6.63∗10−34kgm2s−1(9.11∗10−31kg)(106m/s)=7.28∗10−10m

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 106 kg and moving with velocity of 9.11∗10−31 m/s, and I got the wavelength associated with it as shown below:

λ=hmv=6.63∗10−34kgm2s−1(106kg)(9.11∗10−31m/s)=7.28∗10−10m

This shows that a car or any material object with mass 106kg and moving with velocity 9.11∗10−31m/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 106kg.

Thanks for the question.

Hope it helps you.