1. A ⁶²Ni atom has more mass
2. The protons, neutrons, and electrons have more mass
3. They have exactly the same mass

Binding Energy V

The atomic mass of ⁶²Ni is 61.928 u. ⁶²Ni consists of 28 protons, 34 neutrons, and 28 electrons. If we add up the mass of 28 protons, 34 neutrons, and 28 electrons, how would this combined mass compare to the mass of a ⁶²Ni atom?

1. A Ni-62 nucleus is positively charged
2. Energy is required to hold the Ni-62 nucleus together
3. A Ni-62 nucleus has more kinetic energy than the individual nucleons
4. A Ni-62 nucleus is unstable while the individual nucleons are stable
5. None of the above

Binding Energy VI

The “missing mass” in the ⁶²Ni nucleus can be found in the form of energy. Mass can be transformed into energy by the formula

where c is the speed of light.

Why might a ⁶²Ni nucleus contain more energy than 28 individual protons and 34 individual neutrons?

1. Kilograms (kg)
2. Grams (g)
3. Unified atomic mass units (u)
4. Newtons (N)
5. Any unit of mass will work

Binding Energy VII

We will use the formula E = mc² in order to convert mass defect into binding energy.

Suppose that the constant c (the speed of light) is given in the units meters per second. What must the units of m (mass) be if we want energy to be given in joules?

Binding Energy VIII

Mass and energy are related by the formula , where

​

Also recall that 1 u = 1.6605 · 10^-27 kg.

How much energy (in joules) is equivalent to 1 u of mass?

Binding Energy IX

Binding energies are most often given in terms of millions of electronvolts (MeV), where 1 MeV = 10⁶ eV. The conversion between joules and electronvolts is:

​

How much energy (in MeV) is equivalent to 1 u of mass?

We found in the previous question that

Binding Energy X

Suppose we look up the mass of a ⁴He nucleus in a table of values. We also know A (the mass number of helium) and Z (the atomic number of helium).

How can we calculate the mass defect of ⁴He?

Binding Energy XI

Looking up the mass of helium in a table of values, we find that the mass of a ⁴He nucleus is 4.0015 u. From the previous question, we know we can calculate the mass defect of He by:

​

What is the binding energy per nucleon of ⁴He?

Useful information:

Binding Energy XII

The first ionization energy of helium is the energy required to remove 1 electron from a helium atom. How does this compare to the binding energy per nucleon of helium?

1. The ionization energy of helium is much larger than its binding energy per nucleon
2. The ionization energy of helium is approximately the same as its binding energy per nucleon
3. The ionization energy of helium is much smaller than its binding energy per nucleon

The Binding Energy Curve

The graph above shows the binding energy per nucleon of various isotopes. The maximum of the graph occurs at ⁶²Ni. Most nuclei have a binding energy per nucleon of about 8 MeV.

Binding Energy XIII

The maximum of the binding energy curve occurs at ⁶²Ni. What can we conclude about ⁶²Ni?

1. ⁶²Ni is very stable
2. A ⁶²Ni nucleus has unusually large mass
3. ⁶²Ni tends to decay into lighter products
4. A ⁶²Ni nucleus contains many neutrons
5. ⁶²Ni is often found with high kinetic energy

Binding Energy XIV

Which of the following isotopes has the largest binding energy?

1. ¹H
2. ⁴He
3. ⁶²Ni
4. ¹⁹⁴Pt
5. ²³⁵U

Binding Energy XV

Consider the following nuclear fission reaction:

​

Which side of the reaction will have more mass?

1. Left side
2. Right side
3. Both sides have the same mass

²³⁵U

⁸⁹Kr

¹⁴⁴Ba