A star ending its life with a mass of four to eight times the Sun?s mass is expe

Question

A star ending its life with a mass of four to eight times the Sun?s mass is expected to collapse and then undergo a supernova event. In the remnant that is not carried away by the supernova explosion, protons and electrons combine to form a neutron star with approximately twice the mass of the Sun. Such a star can be thought of as a gigantic atomic nucleus. Assume r = a4^1/3. If a star of mass 3.63 x 10^30 kg is composed entirely of neutrons (mn = 1.67 X 10^-27 kg), what would its radius be? km What time interval is required for the activity of a sample of the radioactive isotope 72 33As to decrease by 90.3% from its original value? The half-life of 72 33As is 26 h. h

Explanation / Answer

4.

mass of star = Ms = 3.63 x 1030 kg

mass of proton = Mp = 1.67 x 10-27 kg

Number of protons =A = Ms / Mp = 3.63 x 1030 / (1.67 x 10-27 ) = 2.2 x 1057

using the formula

r = a A1/3      a    = constant = 1.2 x 10-15

r = (1.2 x 10-15) (2.2 x 1057)1/3

r = 15607.1 m

r = 15.6 km

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