In a laser-tweezer system, the object trapped by the optical laser is the large

Question

In a laser-tweezer system, the object trapped by the optical laser is the large dielectric polystyrene bead (d = 1mm) A biomolecule is a tethered chemically to the surface of the latex bead. Can the laser tweezer trap a single molecule without the assistance of the polystyrene sphere? Estimate the laser power required if 10mW is required to trap a 1 micrometer diameter polystyrene sphere and that the gradient optical forces in the tweezer system are propotional to the polarizability alpha of the trapped object that is in turn propotional to the volume d3 of the potential trapped molecule. Hint: consult W.E. Moerner New direction in single molecule imaging analysis, Proceeding of National Academy of Science, 104 12596-12602 (2007).

Explanation / Answer

No it is not possible because, the gradient optical forces in a tweezers system are proportional to the polarizability of the trapped object, which scales as the volume d 3 (with d the diameter) and the polarizibility of single small protein is very small.

Now, Power required = K (d3) ; where K is constant, d is diameter

so, 10*10^(-3) = K (1*10^(-6))3 -------------------1)

X = K (1*10^(-3))3--------------------------------2)

Dividing,2 with 1 we get

X = 10*10^(-3) *10^(9) = 10*10^(6) W = 10 MW

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