Question

Eleven neutrinos were detected by the Kamioka water Cerenkov detector in Japan, following the explosion of supernova SN1987a. The Kamioka detector had a fiducial mass of 1000 metric tonnes. How many human beings, therefore, actually 'saw' the explosion of SN1987a

Hint - concider the structure of the human eye.

Answer 1

Let us suppose that human eyes are spheres of radius 5 cm.
Then, volume of each eye is approximately4*pi/3 * 5^3 = 523.6 cm^3 = 5.236* 10^(-4) m^3

So, now we can find total volume of all human eyes at ourplanet
We assume that there are approximately 7*10^(9) people atthe moment. So volume of their eyes is

2* 5.236* 10^(-4) m^3*7*10^(9) =7330400 m^3

If 1000 m^3 caught 11 neutrinos,then 7330400 m^3 would catch

11* 7330400/1000 = 80 634,4 neutrinos
supposing every neutrino's cherenkov photons can be saw, wehave that
approximately 80000 human beings,therefore, actually 'saw' the explosion of SN1987a