How to show 400 neutrinos are present?

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SUMMARY

The discussion focuses on calculating the number of neutrinos detected using a specific formula involving water mass and the weight of a human eyeball. The calculation shows that the number of neutrinos detected per kilogram of water is 4*10^-6, leading to a detection of 4*10^-8 neutrinos per eyeball. The user seeks assistance in scaling this calculation to determine how to detect 400 neutrinos, having previously arrived at values of 3.69*10^9 and 4*10^-8 neutrinos through various attempts.

PREREQUISITES
  • Understanding of neutrino physics and detection methods
  • Basic knowledge of unit conversions in physics
  • Familiarity with scientific notation and calculations
  • Concept of mass and volume in relation to neutrino detection
NEXT STEPS
  • Research methods for scaling neutrino detection in large volumes of water
  • Explore neutrino detection technologies such as IceCube Neutrino Observatory
  • Learn about the historical context of neutrino detection, particularly in 1987
  • Study statistical methods for estimating particle detection rates
USEFUL FOR

Physicists, researchers in particle physics, and students studying neutrino detection methods will benefit from this discussion.

hraghav
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Homework Statement
Twelve electron neutrinos from SN 1987A were detected at Kamiokande in Japan. This
experiment consisted of a tank filled with 3x10^6 kg of water and surrounded by photomultiplier tubes to detect the Cerenkov radiation. Scale this to show that about 400 neutrinos could have been “seen” by humans, if we assume that eyeballs are composed primarily of water and weigh about 10 g each.
Relevant Equations
12/3*10^6 kg
4*10^-6 neutrinos * 0.01kg
Number of neutrinos detected per kg of water = 12/3*10^6 kg = 4*10^-6 neutrinos
Neutrinos detected by 1 eyeball = 4*10^-6 neutrinos * 0.01kg = 4*10^-8 neutrinos

I am not sure how to scale this to get 400 neutrinos. I did try multiple ways but either ended up with 3.69*10^9 or 4*10^-8 neutrinos. Could someone please help me with this. Thanks!
 
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