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Solved problems for the chapter:

Mass Defect and Nuclear Binding Energy

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Einstein's Mass-Energy Equation

1. Mass defect

2. Relativistic mass and kinetic energy

3. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:mass_defect_and_nuclear_binding_energy/4551/

Example 1.

When a neutron is captured by a uranium-235 nucleus, the outcome may be represented by the nuclear equation shown below.

- Use the equation to determine the value of .
- State the name of the particle represented by the symbol .
Some data for the nuclei in the reaction are given in the table below.

Use data from the table to
- determine the binding energy, in , of a nucleus of uranium-235,
- show that the binding energy per nucleon of a nucleus of uranium-235 is .
The kinetic energy of the neutron before the reaction is negligible. Use data from (b) to calculate the total energy, in , released in this reaction.

Example 2.

A positron () is a particle that has the same mass as an electron and has a charge of . A positron will interact with an electron to form two -ray photons.

Assuming that the kinetic energy of the positron and the electron is negligible when they interact,

suggest why the two photons will move off in opposite directions with equal energies,
calculate the energy, in , of one of the -ray photons.

A meson is a sub-atomic particle. A stationary meson, which has mass , decays to form two -ray photons. The nuclear equation for this decay is

Explain why the two -ray photons have the same energy.
Determine, for each -ray photon,
- the energy, in joule,
- the wavelength,
- the momentum.

In some power stations, nuclear fission is used as a source of energy.

State what is meant by nuclear fission.
The nuclear fission reaction produces neutrons. In the power station, the neutrons may be absorbed by rods made of boron-10. Complete the nuclear equation for the absorption of a single neutron by a boron-10
nucleus with the emission of an -particle.
Suggest why, when neutrons are absorbed in the boron rods, the rods become hot as a result of this nuclear reaction.

State what is meant by a nuclear fusion reaction.
One nuclear reaction that takes place in the core of the Sun is represented by the equation

Data for the nuclei are given in the table below.
- Calculate the energy, in joules, released in this reaction.
- The temperature in the core of the Sun is approximately . Suggest why such a high temperature is necessary for this reaction to take place.

State what is meant by the binding energy of a nucleus.
A nucleus of uranium‑235 absorbs a neutron and becomes unstable. It then undergoes a fission reaction. One possible reaction is
- Determine the number of neutrons produced in this fission reaction.
- Data for the binding energies per nucleon for this fission reaction are given in the table below.
  
  Calculate the energy released, in , from the fission of one nucleus of uranium‑235.
- The isotope xenon‑142 is unstable. The isotope xenon‑132 is stable. Suggest a reason why xenon‑142 is unstable.

Explain why the mass of an -particle is less than the total mass of two individual protons and two individual neutrons.
An equation for one possible nuclear reaction is

Data for the masses of the nuclei are given in the table below.
- Calculate the mass change, in , associated with this reaction.
- Calculate the energy, in , associated with the mass change in (i).

Explain what is meant by the binding energy of a nucleus.
The following nuclear reaction takes place:
- Determine the values of and .
- State the name of this type of nuclear reaction.
- Compare the binding energy per nucleon of uranium-235 with the binding energy per nucleon of caesium-144.

Explain what is meant by the binding energy of a nucleus.
Data for the masses of some particles are given in the table below.

The energy equivalent of is .
- Calculate the binding energy, in , of a tritium () nucleus
- The total mass of the separate nucleons that make up a polonium-210 () nucleus is . Calculate the binding energy per nucleon of polonium-210.

10.

The incomplete nuclear equation for one possible reaction that takes place in the core of a nuclear reactor is

- State the name given to this type of nuclear reaction.
- Complete the nuclear equation.
The mass defect for the reaction is .
- Calculate the energy, in , equivalent to .
- Suggest two forms of the energy released in this reaction.

11.

One possible nuclear reaction that takes place in a nuclear reactor is given by the equation

Data for the nuclei and particles are given in the table below.

Determine, for this nuclear reaction, the value of .
- Show that the energy equivalent to is .
- Calculate the energy, in , released in this reaction. Give your answer to three significant figures.
Suggest the forms of energy into which the energy calculated in (b)(ii) is transformed.

12.

Define the binding energy of a nucleus.
A stationary nucleus of uranium-238 () decays to form a nucleus of thorium-234 (). An -particle and a gamma-ray photon are emitted. The equation representing the decay is

The masses of the nuclei are given in the table below.
- State the relationship between the binding energies of the nuclei that is consistent with this reaction being energetically possible.
- Calculate, for this reaction
  - the change, in , of the mass,
  - the total energy, in , released.
- State and explain whether the energy of the gamma-ray photon is equal to the energy released in the reaction.

13.

One nuclear reaction that can take place in a nuclear reactor may be represented, in part, by the equation

Data for a nucleus and some particles are given in the table below.

Complete the nuclear reaction shown above.
- Show that the energy equivalent to is .
- Calculate the binding energy per nucleon, in MeV, of lanthanum-139 ().
State and explain whether the binding energy per nucleon of uranium-235 () will be greater, equal to or less than your answer in (b)(ii).

14.

State what is meant by the binding energy of a nucleus.
The table below shows the masses of two sub-atomic particles and a polonium-212 () nucleus.

For the polonium-212 nucleus, determine:
- the mass defect , in
- the binding energy
- the binding energy per nucleon.

15.

State what is meant by the binding energy of a nucleus.
Some masses are shown in the table below.

Calculate the binding energy of a nucleus of lanthanum-141.
The nuclide lanthanum-141 () has a half-life of 3.9 hours. Initially, a radioactive source contains only lanthanum-141. The initial activity of the source is .
- Calculate the time for the activity of the lanthanum-141 to be reduced to .
- Suggest why the total activity of the radioactive source measured at the time calculated in (i) may be greater than .

16.

Define mass defect.
The table below shows the mass defects of three nuclei.

The nuclear fusion process in a particular star is described by

where is a particle that has no mass defect.
- State the name of particle .
- Show that the energy released when one nucleus of is formed in this fusion reaction is .
The star in (b) has a radius of and a luminosity of . All the energy released from the formation of is radiated away from the star. All the energy that is radiated from the star has been released in the formation of . Determine:
- the mass of produced per unit time by the fusion process
- the surface temperature of the star.

17.

State what is meant by the mass defect of a nucleus.
Some masses are shown in the table below.

Show that:
- the energy equivalence of is .
- the binding energy per nucleon of a helium-4 nucleus is .
Isotopes of hydrogen have binding energies per nucleon of less than . Suggest why a nucleus of helium-4 does not spontaneously break down to become nuclei of hydrogen.

18.

State what is meant by nuclear binding energy.
In one type of nuclear process, deuterium () undergoes the reaction

State the name of this type of nuclear process.
The table below shows the masses of the particles involved in the reaction in (b).

Calculate the energy released when of deuterium undergoes the reaction.

19.

The controlled reaction between deuterium () and tritium () has involved ongoing research for many years. The reaction may be summarised as

where .

Binding energies per nucleon are shown in the table below.

Suggest why binding energy per nucleon for the neutron is not quoted.
Calculate the mass defect, in , of a helium nucleus.
- State the name of the type of reaction illustrated by this nuclear equation.
- Determine the binding energy per nucleon, in , of tritium ().

20.

State what is meant by the binding energy of a nucleus.
Show that the energy equivalence of is .
Data for the masses of some particles and nuclei are given in the table below.

Use the data from the table and information from (b) to determine, in ,
- the binding energy of deuterium,
- the binding energy per nucleon of zirconium.