An oxygen nucleus ^{16}_{8}\text{O} has a measured nuclear mass of 15.9906\text{ u}. Given… — JAMB UTME

An oxygen nucleus $^{16}_{8}\text{O}$ has a measured nuclear mass of $15.9906\text{ u}$ . Given that the mass of a proton is $1.0078\text{ u}$ and the mass of a neutron is $1.0087\text{ u}$ , calculate the total binding energy of the nucleus in $\text{MeV}$ . (Take $1\text{ u} = 931.5\text{ MeV}$ )

Answer: 131.71 MeV

Answer

The total binding energy of the oxygen nucleus is

131.71\text{ MeV}

Summing the masses of 8 individual protons and 8 individual neutrons gives

16.1320\text{ u}

. Subtracting the actual nuclear mass of

15.9906\text{ u}

leaves a mass defect of

0.1414\text{ u}

. Multiplying this mass defect by the equivalence constant

931.5\text{ MeV/u}

yields a total binding energy of

131.71\text{ MeV}

Step-by-Step Solution

Calculate the total combined mass of the free constituent nucleons

Mass of 8 protons + 8 neutrons =

8(1.0078\text{ u}) + 8(1.0087\text{ u}) = 8.0624\text{ u} + 8.0696\text{ u} = 16.1320\text{ u}

Oxygen-16 has

Z = 8

protons and

A - Z = 16 - 8 = 8

neutrons.

Calculate the mass defect (

\Delta m

)

\Delta m = 16.1320\text{ u} - 15.9906\text{ u} = 0.1414\text{ u}

Mass defect is the difference between total constituent mass and actual nuclear mass.

Convert mass defect into total binding energy (

E_b

)

E_b = 0.1414\text{ u} \times 931.5\text{ MeV/u} = 131.7141\text{ MeV} \approx 131.71\text{ MeV}

Applying the energy equivalent factor of

931.5\text{ MeV}

per atomic mass unit.

Key Concept

Mass defect and nuclear binding energy equivalence

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