Three Fathoms Observatory
Stewart Yeung

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Studies

 

     

 

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  •     Notes on Nanophysics

 

  • Notes on Nanophysics

    We can have a “feel” of the size of nanometer (nm = 1x10-9 m) :

    1nm = 10 Hydrogen atoms lining up
    2.5 nm = width of one DNA molecule
    1-100 nm = macromolecules; feature sizes of nanomaterials
    Thousands of nm = diameter of one human red blood cell

    Small size does matter :

    1. Large surface-volume ratio (∝ 1/r)

    2. quantum confinement effect

    According to Heisenberg uncertainty principle, ΔP≈ h/ΔL. When electrons, etc. are confined to a region with small ΔL, the increase in ΔP gives rise to an additional confinement kinetic energy of E= ΔP2/2m ≈h2 /2mΔL2 .

    This confinement energy is significant if it is comparable to the kinetic energy of the electron due to its thermal motion, i.e. when

    h2/2mΔL2 > KbT/2. Therefore the quantum confinement effect is significant if ΔL ≈ √(h2/ m KbT). For an electron,  ΔL ≈ 5nm.

     

    First Draft by Stewart Yeung on 15 Dec 2012