Question

Find the Q-value of the reaction: ¹⁹O → ¹⁹F + e + \(\bar \nu\) (atomic mass ¹⁹O = 19.003576u and ¹⁹F = 18.998403u)
1. 2 Mev
2. 8.2 Mev
3. 4.82 Mev
4. 5.8 Mev

Answer 1

Correct Answer - Option 3 : 4.82 Mev

Content: 

Binding Energy: It is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. If the nucleus has a mass M and it contains Z protons and N neutrons then the binding energy of the nucleus is given by

\(B=(Zm_p+Nm_n-M)c^2\)

mp is the mass of a proton, mn is the mass of the neutron, and c= 3 X 108 ms-2 

We can also use atomic masses in place of nuclear masses, to calculate binding energy as follow

\(B=\left(Zm(^1_1H) +Nm_n-m(^{Z+N}_ZX)\right)c^2\)

\(m(^{Z+N}_ZX)\) is the mass of the atom. 

 

The Q-value of a nuclear reaction is numerically equal to the amount of Kinetic energy released.

Q-value = K.E. of product - K.E. of reactant

             = Binding energy of product - Binding energy of reactant 

             = Rest mass energy of reactant - Rest mass-energy of the product

We can express mass in terms of amu and then convert it into MeV using the relation 1uc2  = 931.5 MeV  

Calculation:

Q-value = Binding energy of product - Binding energy of reactant 

 

m(¹⁹O) = 19.003576u 

m(¹⁹F) = 18.998403u 

Q-value = {m(19O) - m(19F) }c² 

              = {19.003576u - 18.998403u}c²

Using uc² = 931.5 MeV 

so, Q-value = 0.005173uc² =0.005173 x 931.5 MeV

                   = 4.82MeV

Option (3) is the correct answer