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

Question

3. Supernovae &Neutron; Stars 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 representa 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

3.1 Molar mass of 56 Fe = 55.935 g/mol

Molar mass of neutrons = 1.008 664 915 88 x 10-3 kg mol-1

now

mass of sun,M =1.989*10^30 kg

so, 2 M = 3.978*10^30 kg

so number of moles of 56Fe, n = 2M/55.935*0.001 = 7.11182622*10^31 moles

hence moles of neutrons = 56 n

so mass deficit = dm

dm = 7.11182622*10^31*0.055935 - 56*7.11182622*10^31*1.008 664 915 88 x 10-3

dm = -0.0391*10^30 kg

energy required = E = dm*c^2 = 3.5218*10^45 J

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