The concept used to solve this problem is gravitational potential Energy.
The equation is given by,
[tex]U=\frac{GM^2}{R}[/tex]
Where U is the gravitational potential energy
M is the mass of object
R is radius (10000m)
G is the unviersal gravitational constant[tex](6.67*10^{-11}m^3/kgs^2)[/tex]
We know that the mass of neutron star is 1.4 times the mass of the sun.
It is known that the mass of sun is [tex]2*10^{30}Kg[/tex]
Replacing the values in our equation we have:
[tex]U= \frac{(6.67*10^{-11})(1.4*(2*10^{30}))}{10000}[/tex]
[tex]U= 5.2*10^{46}J[/tex]
Therefore the energy released in a massive-star supernova explosion is [tex]5.2*10^{46}J[/tex]
To estimate the second point we know that the Total Energy by the Sun is
[tex]E_{sun}=8*10^{35}J[/tex]
We can calculate the ratio between a supernova explosion and our entire main-sequence lifetime energy of the sun.
[tex]U' = \frac{U}{E_{sun}}[/tex]
[tex]U' = \frac{5.2*10^{46}J}{8*10^{35}J}[/tex]
[tex]U' = 6.5*10^{10}[/tex]
Therefore the amount of energy radiated by a supernova explosion is around [tex]10^{10}[/tex] times more than the entire main-sequence lifetime energy of the sun.
