Need help one part B The nuclear reaction that powers the su

Need help one part B

The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p right arrow ^4He + energy. The mass of a helium nucleus is known to be 6.64 x 10^-27 kg How much energy is released in each fusion? Express your answer to one significant figure and include the appropriate units. What fraction of the initial rest mass energy is this energy? Express your answer using one significant figure.

Solution

Total initial mass M = mass of four protons

= [4.002603] * 1.67 * 10^-27

   = 6.6843* 10^-27  kg

Final mass m = 6.64 * 10^-27  kg, so mass defect is,

m = M - m = 6.6843* 10^-27 - 6.64 * 10^-27 = 4.43 * 10^-29   kg

Energy released E = m * c²

   =4.43 * 10^-29* (3x10⁸)²

  =3.987* 10^-12   J

= 4 * 10^-12   J    (approximately)

b.

Total initial mass energy E_i   = M * c²

     = 6.6843* 10^-27* (3x10⁸)²

= 6.01587 * 10^-10   J

hence, E/E_i   = 3.987 * 10^-12 /6.01587 * 10^-10   J

= 6.6 * 10^-3

   = 0.66%

= 0.6% approximately