Berns+Lecture+5+and+6

# Berns+Lecture+5+and+6 - Infertility No fertilization...

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Fertilization No fertilization Infertility
Chapters 1, 7 6,16 & appendix Berns and Greulich 2007 Laser Tweezers (optical trap)

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Laser Tweezers (optical trap) Science Fiction Science Fact 8 micron beads

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How can we explain optical tweezers/trapping from a physics perspective? Not easy! Need to start with: ?
The relativistic mass of a photon A photon at rest, i.e. at speed zero, has no mass. But photons always travel with a speed close or equal to c. For such speedy particles their mass must increase with increasing speed. From Einstein's theory of relativity the mass m at a speed v from the mass at rest, m o is given by m=m o /sqrt(1-v 2 /c 2 ). However, when the speed v of an object approaches c, the term v 2 /c 2 approaches 1 and consequently the square root in the denominator goes to zero. Thus the mass of a particle traveling close to the speed of light increases dramatically. Except when the formal mass m o is zero, as is the case for the photon, the whole expression becomes 0/0. This ratio has to be carefully calculated by alternative means. The alternative approach uses E=m.c 2 Physics tells us that a photon at rest has no mass, but a photon moving at the speed of light does have mass. So we can apply Einstein’s theory of relativity and his most famous equation:

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E=m.c 2 which implies that energy is always correlated with a mass m. m = E/c 2 =(h/ λ ).(1/c) one can calculate, for example, that a green photon (with a wavelength of 500 nm) carries a relativistic mass of 4.10 -33 g, which is about 1 :225000 of the mass of an electron at rest (9.10 -28 g).
Thus photons have a mass m and travel at a velocity c and therefore they have a translational momentum p . p = m.c = E/c = (h/ λ ) E = energy h = Planck’s constant

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Therefore, if photons have both mass and momentum, the momentum can be transferred to other bodies, and we call this radiation pressure: photons can exert force.
HOW SIGNIFICANT IS RADIATION PRESSURE? The effects of light pressure are quite small. For example, a car in sunlight is less than a millipound heavier than in the shade. The force which is exerted on the planet Earth by sunlight corresponds to a mass of ten thousand tons at the Earth's surface, large but not dramatic for such a big object. When a continuous laser with moderate power of 1Watt is focused to the diffraction limit, it can exert a force of approximately only 5nN (nanonewton). But microscopic objects have very small masses which can be accelerated dramatically even by such small forces. For example, a bacterium with a diameter of 1 μ m has a weight of one picogram. By a force of 5 nN it is accelerated with 3.3x10 6 m/s 2 or 30000-fold gravitational acceleration.

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## This note was uploaded on 12/13/2011 for the course BIOSCI 130 taught by Professor Berns during the Fall '11 term at UC Irvine.

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Berns+Lecture+5+and+6 - Infertility No fertilization...

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