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Opus in profectus

Quantum Flavordynamics

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Practice

practice problem 1

Two related problems in solar physics…
  1. How many solar neutrinos pass through your fingernail every second?
  2. How many solar photons land on your finger every second when you are in direct sunlight?

solution

  1. Use the total power of the sun, which includes the electromagnetic (3.85 × 1026 W) and neutrino (0.089 × 1026 W) luminosities. Divide by the energy released per reaction in the proton–proton chain (26.7 MeV). Spread the radiation over the surface of a sphere (r2) the size of the Earth's orbit (one astronomical unit). Multiply by the area of a fingernail (1 cm2) and the time of one second (1 s). Double this number, since the proton–proton chain releases two neutrinos per reaction.

    2(3.939 × 1026 W)(1 s)(1 cm2)  
    (26.7 MeV)(1 astronomical unit)2  
     = 6.5 × 1010  
     

    That's 65 billion neutrinos through your fingernail every second. In order to capture the full number, you need to hold your fingernail perpendicular to the direction of the sun, however. Tilt your fingernail and the number decreases. This number is not significantly affected by the material between your fingernail and the sun, however. Even at midnight, when the whole mass of the Earth is between you and the sun, 65 billion neutrinos pass through your fingernail every second. Neutrinos interact with matter via the weak force, which means they only interact on "direct hits" with certain subatomic particles, which means they basically interact with nothing.

  2. Use the electromagnetic luminosity of the sun (3.85 × 1026 W). Divide by the energy (E = hc) of a photon near the peak wavelength (550 nm). Spread the radiation over the surface of a sphere (r2) the size of the Earth's orbit (one astronomical unit). Multiply by the area of a fingernail (1 cm2) and the time of one second (1 s).

    (3.85 × 1026 W)(1 s)(1 cm2)(550 nm)  
    (hc/550 nm)(1 astronomical unit)2  
     = 3.8 × 1017  
     

    That's 380 quadrillion photons landing on your fingernail every second. As with the neutrino number calculated above, this number assumes the fingernail is aligned perpendicular to the direction of the sun. Unlike the neutrino number, however, this number is greatly affected by the material between the fingernail and the sun. The atmosphere absorbs some of the sun's photons even when the sky is crystal clear. Aerosols like dust and water droplets absorb some more. And of course at midnight, when the Earth is between you and the sun, absolutely no photons make the direct trip from the sun to your fingernail. Photons interact with matter via the electromagnetic force, which means they interact with anything with charge, which means they basically interact with everything.

practice problem 2

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solution

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practice problem 3

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solution

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practice problem 4

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solution

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