Mass defect & binding energy

Explain what is meant by nuclear binding energy of a nucleus.

Explain why isotopes with low mass numbers, such as hydrogen, are those which undergo nuclear fusion.

Use the diagram given at the start of this question to show that, for the reaction of deuterium and tritium, the energy released in each fusion event is approximately 3 × 10^–12 J.

Determine the charge of the missing particle.

The missing particle is a lepton. Name this lepton.

In the fusion reaction above, determine the total number of up quarks at the start of the reaction.

Large power stations generate an electrical power of about 1 GW.

Current methods of energy production that use nuclear fusion are unable to produce enough energy for large-scale energy production. A proposed method of controlling nuclear fusion is inertial confinement fusion (ICF). ICF uses a large number of powerful lasers to create the high temperatures required for nuclear fusion to occur.

One ICF experiment uses a network of capacitors to store the energy needed to power the lasers. When the network is fully charged:

• potential difference across the network = 24 kV

• total energy stored in the network = 400 MJ

Calculate the total capacitance, C, of the network.

Explain why the individual capacitors in the network should be connected in parallel in order to produce this total capacitance.

The total stored energy must be released in a time of less than 1 millisecond.

Explain, using a calculation, why the lasers are powered by the network of capacitors instead of being connected directly to the mains electricity supply.

The fusion reaction in the ICF experiment is

Calculate the number of fusion reactions that must occur for the energy released by fusion to be equal to the electrical energy stored in the network of capacitors.

• mass of deuterium = 2.014102 u

• mass of tritium = 3.016049 u

• mass of alpha particle = 4.002603 u

• mass of neutron = 1.008665 u

Explain the function of the control rods and the moderator in a nuclear fission reactor.

A researcher is doing an experiment on a radioactive solution in a thin glass tube. The solution has two radioactive materials X and Y. The table below shows some data on these two materials.

The solution has the same number of nuclei of X and Y at the start.

State and explain which material has the greatest activity at the start.

State why it is dangerous for the researcher to handle the test tube with bare hands.

Carbon-14 (¹⁴₆C) is produced in the upper atmosphere of the Earth by collisions between nitrogen nuclei and fast-moving neutrons. The nuclear transformation equation below shows the formation of a single carbon-14 nucleus.

State the proton number of particle X.

Use the data below to determine the binding energy per nucleon of the¹⁴₆C nucleus. Write your answer to 3 significant figures.

• mass of neutron = 1.675 × 10^–27 kg

• mass of proton = 1.673 × 10^–27 kg

• mass of¹⁴₆C nucleus = 14.000 u

• 1 u = 1.66 × 10^–27 kg

binding energy per nucleon =........ J per nucleon

X-ray photons interact with atoms.

The attenuation coefficient against lg(photon energy) graphs for simple scattering (S), photoelectric effect (PE), Compton effect (C) and pair production (PP) are shown below.

With the help of a calculation, explain the minimum photon energy shown on the graph for pair production.

This question is about the Sun and its radiation.

Use the data below to show that the luminosity of the Sun is about 4 × 10²⁶ W. (a) (i)

• radius of Sun = 7.0 × 10⁸ m

• surface temperature of Sun = 5800 K

Sirius, the brightest star in the night sky, has a luminosity 25 times greater than that of the Sun. It has diameter 1.7 times greater than that of the Sun.

Calculate the surface temperature T of Sirius.

The key on Fig. 21 shows whether a nucleus is stable, emits a beta-plus particle or emits a beta-minus particle to become stable.

For Z = 7, suggest in terms of N why an isotope may emit

a beta-minus particle

a beta-plus particle.

Inside a nuclear reactor, fission reactions are controlled and chain reactions are prevented. A typical fission reaction of the uranium-235 nucleus (²³⁵₉₂U) is illustrated below.

The neutron triggering the fission reaction moves slowly. The neutrons produced in the fission reaction move fast.

Describe what is meant by chain reaction.

Explain how chain reactions are prevented inside a nuclear reactor.

The energy released in each fission reaction is equivalent to a decrease in mass of 0.19 u. A fuel rod in a nuclear reactor contains 3.0% of uranium-235 by mass.

Estimate the total energy produced from 1.0 kg of fuel rod.

molar mass of uranium-235 = 0.235 kg mol^–1 1 u = 1.66 × 10^–27 kg

Explain why a high-speed proton is necessary to trigger the nuclear reaction shown above.

Estimate the minimum wavelength λ of the gamma ray photon ().

Fluorine-18 is a positron emitter. Name a medical imaging technique that uses fluorine-18 and state one benefit of the technique.

Describe how the components of a computerised axial tomography (CAT) scanner can produce high-quality images of the internal structures of a patient.

Stars produce energy by nuclear fusion. One particular fusion reaction between two protons (¹₁H) is shown below.

In this reaction 2.2 MeV of energy is released.

Only one of the particles shown in the reaction has binding energy. Determine the binding energy per nucleon of this particle. Explain your answer.

Explain why high temperatures are necessary for fusion reactions to occur in stars.

A gamma photon in a star can spontaneously create an electron-positron pair. Calculate the maximum wavelength of a gamma photon for this creation event.