Supernovae &Neutron; Stars 3. 3.1. (ALL) When an iron stellar core collapses in

Question

Supernovae &Neutron; Stars 3. 3.1. (ALL) When an iron stellar core collapses in a supernova event, it converts all of the iron into neutrons. However the resulting neutrons each individually represent a higher-energy state than the iron nuclei. How much energy does it take to convert 2 Mo of 5626Fe into neutrons, assuming that each neutron masses the same as it would in free space? 3.2. (ALL) How does the above value compare to the total amount of energy that was released in creating the 626Fe from hydrogen in the first place? 3.3. (ALL) How much energy is liberated-by the gravitational collapse of a the aforemen- tioned 2 Mo core from a radius of 1 Rg down to a radius of 20 km? Assume constant density (not so bad of an assumption in this case).

Explanation / Answer

3.2

Number of electrons in one iron molecule = 26

Mass of electron

= 9.1 ×10-31 kg

Energy required for one molecule

E = mc2

= 26×9.31×10-31 ×9.8×( 2.99 ×108 )2 W

=2.12 ×10-11 W

For two molecules =4.24 ×10-11 W

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