Question

Calculate the separation energy of ¹⁶O into an alpha particle and a ¹²C nucleus

Calculate the separation energy of ¹⁶O into an proton and a ¹⁵N nucleus

Answer 1

Since no values of the masses have been provided, I am using the standard values ( as provided on wikipaedia if you wish to look ) as

Mass of alpha particle = 4.001506179 u

Mass of O¹⁶ atom = 15.99903 u

Mass of C¹² atom = 12.0096u

Mass of proton = 1.007276467 u

Mass of N atom = 15.000108898 u

1. The associated reaction is

O¹⁶ ₂He⁴ + C¹²

Mass of reactants = 15.99903 u

Mass of products = 4.001506179 + 12.0096 = 16.011106179 u

= 15.99903 - 16.011106179 = -0.012076179 u

Energy of separation is given by the Einstein's relation.

=

Where is in kg and c is in m/s.

from the Einstein relation 1 u (or amu) is equivalent to 931 MeV.

= 931 when is in u.

= 931 X (-0.012076179)

= -11.242922649 MeV

'-' sign suggests that the energy must be given to the oxyen atom to break into alpha particle and C nucleus.

2. The associated reaction is

O¹⁶ N¹⁵ + p

Mass of reactants = 15.99903 u

mass of products = 1.007276467 + 15.000108898

= 16.007385365 u

= 15.99903 - 16.007385365

= -0.008355365 u

From the above mentioned relation in problem 1

= 931 X

= 931 X (-0.008355365)

= -7.778844815 MeV

the significance of the '-' sign has been explained in the previous problem.

any queries or doubts are welcome. Feel free to ask for any explanation related to the question.