Question

In the reaction p + 19F -> α + 16O, the masses are: m(p) = 1.007825 u, m(α) = 4.002603 u, m(F) = 18.998405 u, m(O) = 15.994915 u. Calculate the Q of the reaction from these data.

Answer 1

The Q of the nuclear reaction p + 19F -> α + 16O is calculated by finding the mass defect and converting it into energy using Einstein's mass-energy equivalence formula, resulting in an energy change of approximately 4.39 MeV.

Step-by-step explanation:

To calculate the Q of the nuclear reaction p + 19F -> α + 16O, we first need to determine the mass change that occurs during the reaction and then convert that change into energy. We begin by summing the masses of the reactants and products:

Mass of reactants = m(p) + m(19F) = 1.007825 u + 18.998405 u = 20.006230 u

Mass of products = m(α) + m(16O) = 4.002603 u + 15.994915 u = 20.001518 u

The change in mass (mass defect) is then calculated by subtracting the mass of the products from the mass of the reactants:

Mass defect = Mass of reactants - Mass of products = 20.006230 u - 20.001518 u = 0.004712 u

To convert the mass defect into energy, we use Einstein's mass-energy equivalence formula E = mc², with c² being the square of the speed of light in vacuum. We then multiply the mass defect by the conversion factor from atomic mass units to energy (931.5 MeV/c² per u). Therefore, the energy release (Q) of the reaction is:

Q = Mass defect × (931.5 MeV/c²/u)

Q = 0.004712 u × 931.5 MeV/u = 4.38922 MeV

The energy change of this nuclear reaction is approximately 4.39 MeV.