12.2 – Nuclear physics

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

The accepted value of the diameter of the carbon-12 nucleus is $4.94\times {10}^{-15} \mathrm{m}$. Estimate the angle ${\theta }_0$ at which the minimum of the intensity is formed.

Plot the position of magnesium-24 on the graph.

Plot the position of magnesium-24 on the graph.

Plot the position of magnesium-24 on the graph.

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

Explain what may be deduced about the energy of the electron in the β^– decay.

Explain what may be deduced about the energy of the electron in the β^– decay.

Explain what may be deduced about the energy of the electron in the β^– decay.

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

The graph shows the variation of the natural log of activity, ln (activity), against time for a radioactive nuclide.

What is the decay constant, in days^–1, of the radioactive nuclide?

A.   $\frac{1}{6}$

B.   $\frac{1}{3}$

C.   3

D.   6

The graph shows the variation of the natural log of activity, ln (activity), against time for a radioactive nuclide.

What is the decay constant, in days^–1, of the radioactive nuclide?

A.   $\frac{1}{6}$

B.   $\frac{1}{3}$

C.   3

D.   6

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

In a fresh pure sample of ${}_{15}^{32}\text{P}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}\text{P}$.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

Show that the nuclear radius of phosphorus-31 (${}_{15}^{31}\text{P}$) is about 4 fm.

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Estimate, using the result from (a)(i), the nuclear radius of thorium-232 $\left({}_{90}^{232}\text{Th}\right)$.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

Suggest one reason why a beam of electrons is better for investigating the size of a nucleus than a beam of alpha particles of the same energy.

The nucleus of the isotope hydrogen-2 has a radius R and a density $\rho$.

What are the approximate radius and density of a nucleus of oxygen-16?

The nucleus of the isotope hydrogen-2 has a radius R and a density $\rho$.

What are the approximate radius and density of a nucleus of oxygen-16?

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

Outline why the particles must be accelerated to high energies in scattering experiments.

Outline why the particles must be accelerated to high energies in scattering experiments.

Outline why the particles must be accelerated to high energies in scattering experiments.

Determine the radius of the magnesium-24 nucleus.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

Two samples X and Y of different radioactive isotopes have the same initial activity. Sample X has twice the number of atoms as sample Y. The half-life of X is T. What is the half-life of Y?

A.     2T

B.     T

C.     $\frac{T}{2}$

D.     $\frac{T}{4}$

Two samples X and Y of different radioactive isotopes have the same initial activity. Sample X has twice the number of atoms as sample Y. The half-life of X is T. What is the half-life of Y?

A.     2T

B.     T

C.     $\frac{T}{2}$

D.     $\frac{T}{4}$

Calculate the wavelength of the gamma ray photon in (d)(ii).

Calculate the wavelength of the gamma ray photon in (d)(ii).

Calculate the wavelength of the gamma ray photon in (d)(ii).

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

${}_{15}^{32}\text{P}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

Use the graph to show that the nuclear radius of silicon-30 is about 4 fm.

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

The unstable lead nuclide has a half-life of 15 × 10⁶ years. A sample initially contains 2.0 μmol of the lead nuclide. Calculate the number of thallium nuclei being formed each second 30 × 10⁶ years later.

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

Estimate the power, in kW, that is available from the plutonium at launch.

Estimate the power, in kW, that is available from the plutonium at launch.

Estimate the power, in kW, that is available from the plutonium at launch.

The spacecraft will take 7.2 years (2.3 × 10⁸ s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

The spacecraft will take 7.2 years (2.3 × 10⁸ s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

The spacecraft will take 7.2 years (2.3 × 10⁸ s) to reach a planet in the solar system. Estimate the power available to the spacecraft when it gets to the planet.

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

Estimate, using the result in (a)(iii), the volume of a tin-118 $\left({}_{50}{}^{118}\text{Sn}\right)$ nucleus. State your answer to an appropriate number of significant figures.

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

The half-life of potassium-40 is 1.3 × 10⁹ years. Estimate the age of the rock sample.

The half-life of potassium-40 is 1.3 × 10⁹ years. Estimate the age of the rock sample.

The half-life of potassium-40 is 1.3 × 10⁹ years. Estimate the age of the rock sample.

Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.

Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.

Outline how the decay constant of potassium-40 was determined in the laboratory for a pure sample of the nuclide.

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

A group of students perform an experiment to find the refractive index of a glass block. They measure various values of the angle of incidence i and angle of refraction r for a ray entering the glass from air. They plot a graph of the sin r against sin i.

They determine the gradient of the graph to be m.

Which of the following gives the critical angle of the glass?

A.  sin⁻¹(m)

B.  sin⁻¹$\left(\frac{1}{m}\right)$

C.  m

D.  $\frac{1}{m}$

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.

Deduce the unit of μ in terms of fundamental SI units.

Deduce the unit of μ in terms of fundamental SI units.

Deduce the unit of μ in terms of fundamental SI units.

Deduce the unit of μ in terms of fundamental SI units.

Deduce the unit of μ in terms of fundamental SI units.

Deduce the unit of μ in terms of fundamental SI units.

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.

Identify with ticks [✓] in the table, the forces that can act on electrons and the forces that can act on quarks.