Question

Supernova. In addition to the flash of light, a core-collapse supernova also emits

enormous amounts of neutrinos, through the reaction: electron + proton → neutron + neutrino.

Imagine that a supernova occurs in the Milky Way, at a distance of 10 kpc from Earth,

releasing 1057 neutrinos isotropically.

a. How many of these supernova neutrinos would be expected to pass through Earth?

b. When it was in operation, the Sudbury Neutrino Observatory (SNO) had an active volume

of 1000 metric tonnes (1 million kg) of heavy water D2O contained in a spherical acrylic

vessel 6 metres in radius. Neutrinos interact so weakly with matter that only about one in

1015 supernova neutrinos passing through the SNO detector were expected to be detected.

About how many neutrinos from the above supernova would have been detected by SNO?

Answer 1

(a) About 10^(57) Neutrinos are released isotropically, therefore as it travels it spreads out, and eventually falls on earth, Number of neutrinos falling on earth is,

d is the distance of earth from supernova, Substituting values we get,

(b) Of the neutrinos, falling on earth, the about of neutrinos passing through SNO is given by,

Substituting values,

Only, one in 10^(15) neutrinos are detected, hence the number of detected neutrinos is,