Mass defect and binding energy

Polonium-210 decays into lead-206 by emitting an alpha particle.

mass of nucleus of polonium-210 = 209.983 u mass of nucleus of lead-206 = 205.975 u mass of alpha particle = 4.003 u

Assume that the recoil speed of the lead nucleus is negligible.

What is the kinetic energy of the emitted alpha particle?

The plot of average binding energy per nucleon is shown. P, Q and R indicate regions of the plot.

In which region or regions labelled on the plot do nuclei undergo fission to release energy?

The following reaction occurs when a proton and a carbon-13 13C 6 nucleus fuse. 13 1 14

mass of 13 6C nucleus = 13.00007 u

mass of 14 7 N nucleus = 13.99925 u

mass of proton = 1.00728 u

What is the quantity of energy released?

5.6 kW h of heat energy is released when 1.0 kg of wood pellets are burnt in a power station.

What is the mass lost in burning 1.0 kg of wood pellets?

The mass of fuel in a nuclear reactor decreases at a rate of 4.0 × 10⁻⁶ kg per hour.

What is the rate at which energy is transferred due to nuclear fission?

Fission and fusion are two processes that can result in the transfer of binding energy from nuclei.

State what is meant by the binding energy of a nucleus.

Calculate, in MeV, the binding energy for a nucleus of iron 5626Fe.

Figure 10 shows a graph of average binding energy per nucleon against nucleon number for common nuclides.

The nuclide labelled X in Figure 10 undergoes fission.

Annotate Figure 10 with F₁ and F₂ to show one possible pair of nuclides resulting from the fission of X.

Figure 11 shows a graph of N against Z for stable nuclides.

Deduce the likely initial mode of decay of F₁ and F₂. Refer to Figure 11 in your answer.

Section B

Each of Questions 07 to 31 is followed by four responses, A, B, C and D.

For each question select the best response.

Explain, in terms of binding energy, why energy can be released when two nuclei undergo nuclear fusion.

During the collapse of a supermassive star, helium-3 and oxygen-17 fuse to release energy. The equation for this reaction is

3 17 20

Table 2 gives data for these nuclei.

Calculate, in J, the energy released when this reaction occurs.

One model of nuclear fusion suggests that fusion happens when nuclei touch.

Initially the helium nucleus and oxygen nucleus are separated so that the force between them is negligible. They move towards each other until they fuse. Fusion occurs when their centres are separated by a distance of 5.1 × 10⁻¹⁵ m.

Figure 10 shows the initial positions and final positions of the nuclei.

Calculate the total change in electrostatic potential energy between the initial positions and final positions of the nuclei.

3He 34 S 17 O can undergo fusion reactions with either or at the same temperature 2 16 8 in a star.

The nucleus has properties that depend on its proton number and its nucleon number. These properties affect the fusion reaction.

34 3 Discuss, for this star, how these properties affect the rate of fusion of S with He 16 2 17 3 compared to the rate of fusion of 8 O with 2 He.

In the core of a nuclear reactor, the mass of fuel decreases at a rate of 9.0 × 10⁻⁶ kg hour⁻¹ due to nuclear reactions.

What is the maximum power output of the reactor?

The table shows the masses of three particles.

What is the mass difference of a⁷₃Li nucleus?

The mass of the fuel in a fission reactor decreases at a rate of 6.0 × 10⁻⁶ kg hour⁻¹.

What is the maximum possible power output of the reactor?

A thermal nuclear reactor uses a moderator to lower the kinetic energy of fast-moving neutrons.

Explain why the kinetic energy of neutrons must be reduced in a thermal nuclear reactor.

As a result of a collision with an atom of a particular moderator, a neutron loses 63% of its kinetic energy.

A neutron has an initial kinetic energy of 2.0 MeV.

Calculate the kinetic energy of the neutron after five collisions.

The kinetic energy of a neutron in a thermal nuclear reactor is reduced from about 2 MeV to about 1 eV.

Explain why the number of collisions needed to do this depends on the nucleon number of the moderator atoms.

One fission process which can occur in a thermal nuclear reactor is represented by the equation

235 1 142 90 1 U + n = Xe + Sr + 4 n 92 0 54 38 0

Calculate in MeV the energy released in this fission process.

Many magazine and newspaper articles focus on the risks of using nuclear power.

State three benefits of using nuclear power.

Section B

Each of Questions 07 to 31 is followed by four responses, A, B, C and D.

For each question select the best response.

A deuterium nucleus and a tritium nucleus fuse together to form a helium nucleus and a particle X. The equation for this process is:

2 3 4

What is X ?

During a single fission event of uranium-235 in a nuclear reactor the total mass lost is 0.23 u. The reactor is 25% efficient.

How many events per second are required to generate 900 MW of power?

Calculate the binding energy, in MeV, of a nucleus of⁵⁹₂₇ Co.

A nucleus of iron Fe-59 decays into a stable nucleus of cobalt Co-59. It decays by ⁻ emission followed by the emission of -radiation as the Co-59 nucleus de-excites into its ground state.

The total energy released when the Fe-59 nucleus decays is 2.52 × 10⁻¹³ J.

The Fe-59 nucleus can decay to one of three excited states of the cobalt-59 nucleus as shown in Figure 5. The energies of the excited states are shown relative to the ground state.

Calculate the maximum possible kinetic energy, in MeV, of the ⁻ particle emitted when the Fe-59 nucleus decays into an excited state that has energy above the ground state.

Following the production of excited states of⁵⁹₂₇ Co, -radiation of discrete wavelengths is emitted.

State the maximum number of discrete wavelengths that could be emitted.

Calculate the longest wavelength of the emitted -radiation.

longest wavelength = m 9

What is the energy released in this process?