E.3 Radioactive decay

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

Calculate, in s⁻¹, the initial activity of the sample.

Calculate, in s⁻¹, the initial activity of the sample.

Calculate, in s⁻¹, the initial activity of the sample.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Estimate the fraction of tritium remaining after one year.

Estimate the fraction of tritium remaining after one year.

Estimate the fraction of tritium remaining after one year.

Explain how the difference in part (b)(ii) arises.

Explain how the difference in part (b)(ii) arises.

Explain how the difference in part (b)(ii) arises.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Calculate, in MeV, the energy released in the reaction.

Calculate, in MeV, the energy released in the reaction.

Calculate, in MeV, the energy released in the reaction.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

A nucleus of krypton (Kr) decays to a nucleus of bromine (Br) according to the equation

${}_{36}{}^{84}\text{Kr}\to {}_{35}{}^{84}\text{Br}+\text{Y}+\text{Z}$

What are Y and Z?

A nucleus of krypton (Kr) decays to a nucleus of bromine (Br) according to the equation

${}_{36}{}^{84}\text{Kr}\to {}_{35}{}^{84}\text{Br}+\text{Y}+\text{Z}$

What are Y and Z?

The unified atomic mass unit, u, is a non-SI unit usually used by scientists to state atomic masses.

What is u?

A.  It is the mean of the masses of a proton and a neutron.

B.  It is the mean of the masses of protons and neutrons in all chemical elements.

C.  It is $\frac{1}{16}$ the mass of an ${}_8{}^{16}\text{O}$ atom.

D.  It is $\frac{1}{12}$ the mass of a ${}_6{}^{12}\text{C}$ atom.

The unified atomic mass unit, u, is a non-SI unit usually used by scientists to state atomic masses.

What is u?

A.  It is the mean of the masses of a proton and a neutron.

B.  It is the mean of the masses of protons and neutrons in all chemical elements.

C.  It is $\frac{1}{16}$ the mass of an ${}_8{}^{16}\text{O}$ atom.

D.  It is $\frac{1}{12}$ the mass of a ${}_6{}^{12}\text{C}$ atom.

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

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.

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

The carbon isotope $\frac{14}{6}$C is radioactive. It decays according to the equation

$\frac{14}{6}$C → $\frac{14}{7}$N + X + Y

What are X and Y?

The carbon isotope $\frac{14}{6}$C is radioactive. It decays according to the equation

$\frac{14}{6}$C → $\frac{14}{7}$N + X + Y

What are X and Y?

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

Which property of a nuclide does not change as a result of beta decay?

A. Nucleon number

B. Neutron number

C. Proton number

D. Charge

Which property of a nuclide does not change as a result of beta decay?

A. Nucleon number

B. Neutron number

C. Proton number

D. Charge

The rest mass of the helium isotope ${}_2^3\text{He}$ is m.

Which expression gives the binding energy per nucleon for ${}_2^3\text{He}$?

A. $\frac{(2m_p+m_n+m)c^2}{3}$

B. $\frac{(2m_p+m_n-m)c^2}{3}$

C. $(2m_p+m_n+m)c^2$

D. $(2m_p+m_n-m)c^2$

The rest mass of the helium isotope ${}_2^3\text{He}$ is m.

Which expression gives the binding energy per nucleon for ${}_2^3\text{He}$?

A. $\frac{(2m_p+m_n+m)c^2}{3}$

B. $\frac{(2m_p+m_n-m)c^2}{3}$

C. $(2m_p+m_n+m)c^2$

D. $(2m_p+m_n-m)c^2$

A radioactive nuclide with atomic number Z undergoes a process of beta-plus (β⁺) decay. What is the atomic number for the nuclide produced and what is another particle emitted during the decay?

A radioactive nuclide with atomic number Z undergoes a process of beta-plus (β⁺) decay. What is the atomic number for the nuclide produced and what is another particle emitted during the decay?

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

Estimate, in Bq, the initial activity of the sample.

Estimate, in Bq, the initial activity of the sample.

Estimate, in Bq, the initial activity of the sample.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus (β^–) decay. In Route 2 β^– decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A.  Q and S are different isotopes of the same element.

B.  The mass numbers of X and R are the same.

C.  The atomic numbers of P and R are the same.

D.  X and R are different isotopes of the same element.

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus (β^–) decay. In Route 2 β^– decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A.  Q and S are different isotopes of the same element.

B.  The mass numbers of X and R are the same.

C.  The atomic numbers of P and R are the same.

D.  X and R are different isotopes of the same element.

Gamma ($\gamma$) radiation

A.  is deflected by a magnetic field.

B.  affects a photographic plate.

C.  originates in the electron cloud outside a nucleus.

D.  is deflected by an electric field.

Gamma ($\gamma$) radiation

A.  is deflected by a magnetic field.

B.  affects a photographic plate.

C.  originates in the electron cloud outside a nucleus.

D.  is deflected by an electric field.

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.  $t_{\frac{1}{2}}$

X is a radioactive nuclide that decays to a stable nuclide. The activity of X falls to $\frac{1}{16}$th of its original value in 32 s.
What is the half-life of X?

A.  2 s

B.  4 s

C.  8 s

D.  16 s

X is a radioactive nuclide that decays to a stable nuclide. The activity of X falls to $\frac{1}{16}$th of its original value in 32 s.
What is the half-life of X?

A.  2 s

B.  4 s

C.  8 s

D.  16 s

Calculate the binding energy per nucleon for uranium-238.

Calculate the binding energy per nucleon for uranium-238.

Calculate the binding energy per nucleon for uranium-238.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

Which graph shows the variation of activity $A$ with time $t$ for a radioactive nuclide?

Which graph shows the variation of activity $A$ with time $t$ for a radioactive nuclide?

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

A sample of a pure radioactive nuclide initially contains $N_0$ atoms. The initial activity of the sample is $A_0$.

A second sample of the same nuclide initially contains $2N_0$ atoms.

What is the activity of the second sample after three half lives?

A.  $\frac{A_0}{2}$

B.  $\frac{A_0}{4}$

C.  $\frac{A_0}{6}$

D.  $\frac{A_0}{8}$

A sample of a pure radioactive nuclide initially contains $N_0$ atoms. The initial activity of the sample is $A_0$.

A second sample of the same nuclide initially contains $2N_0$ atoms.

What is the activity of the second sample after three half lives?

A.  $\frac{A_0}{2}$

B.  $\frac{A_0}{4}$

C.  $\frac{A_0}{6}$

D.  $\frac{A_0}{8}$

Three particles are produced when the nuclide ${}_{12}{}^{23}\text{Mg}$ undergoes beta-plus (β⁺) decay. What are two of these particles?

A. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\text{v}_{\text{e}}$

B. ${}_{-1}{}^0\text{e}$ and ${}_0{}^0\text{v}_{\text{e}}$

C. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

D. ${}_1{}^0\text{e}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

Three particles are produced when the nuclide ${}_{12}{}^{23}\text{Mg}$ undergoes beta-plus (β⁺) decay. What are two of these particles?

A. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\text{v}_{\text{e}}$

B. ${}_{-1}{}^0\text{e}$ and ${}_0{}^0\text{v}_{\text{e}}$

C. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

D. ${}_1{}^0\text{e}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

When a high-energy $\alpha$-particle collides with a beryllium-9 (${}_4{}^9\text{Be}$) nucleus, a nucleus of carbon $\left(\text{Z}=6\right)$ may be produced. What are the products of this reaction?

When a high-energy $\alpha$-particle collides with a beryllium-9 (${}_4{}^9\text{Be}$) nucleus, a nucleus of carbon $\left(\text{Z}=6\right)$ may be produced. What are the products of this reaction?

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?

A pure sample of radioactive nuclide $\text{X}$ decays into a stable nuclide $\text{Y}$.

What is $\frac{\text{number of atoms of Y}}{\text{number of atoms of X}}$ after two half-lives?

A.  1

B.  2

C.  3

D.  4

A pure sample of radioactive nuclide $\text{X}$ decays into a stable nuclide $\text{Y}$.

What is $\frac{\text{number of atoms of Y}}{\text{number of atoms of X}}$ after two half-lives?

A.  1

B.  2

C.  3

D.  4

The mass of a nucleus of iron-56 (${}_{26}{}^{56}\text{Fe}$) is M.

What is the mass defect of the nucleus of iron-56?

A.  M − 26m_p − 56m_n

B.  26m_p + 30m_n − M

C.  M − 26m_p − 56m_n − 26m_e

D.  26m_p + 30m_n + 26m_e − M

The mass of a nucleus of iron-56 (${}_{26}{}^{56}\text{Fe}$) is M.

What is the mass defect of the nucleus of iron-56?

A.  M − 26m_p − 56m_n

B.  26m_p + 30m_n − M

C.  M − 26m_p − 56m_n − 26m_e

D.  26m_p + 30m_n + 26m_e − M

A pure sample of iodine-131 decays into xenon with a half-life of 8 days.

What is $\frac{\text{number of iodine atoms remaining}}{\text{number of xenon atoms formed}}$ after 24 days?

A.  $\frac{1}{8}$

B.  $\frac{1}{7}$

C.  $\frac{7}{8}$

D.  $\frac{8}{7}$

A pure sample of iodine-131 decays into xenon with a half-life of 8 days.

What is $\frac{\text{number of iodine atoms remaining}}{\text{number of xenon atoms formed}}$ after 24 days?

A.  $\frac{1}{8}$

B.  $\frac{1}{7}$

C.  $\frac{7}{8}$

D.  $\frac{8}{7}$

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.

A radioactive nuclide X decays into a nuclide Y. The graph shows the variation with time of the activity A of X. X and Y have the same nucleon number.

What is true about nuclide X?

A.  alpha (α) emitter with a half-life of t

B.  alpha (α) emitter with a half-life of 2t

C.  beta-minus (β⁻) emitter with a half-life of t

D.  beta-minus (β⁻) emitter with a half-life of 2t

A radioactive nuclide X decays into a nuclide Y. The graph shows the variation with time of the activity A of X. X and Y have the same nucleon number.

What is true about nuclide X?

A.  alpha (α) emitter with a half-life of t

B.  alpha (α) emitter with a half-life of 2t

C.  beta-minus (β⁻) emitter with a half-life of t

D.  beta-minus (β⁻) emitter with a half-life of 2t

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.  $4$

${}_{92}{}^{238}\text{U}$ undergoes an alpha decay, followed by a beta-minus decay. What is the number of protons and neutrons in the resulting nuclide?

${}_{92}{}^{238}\text{U}$ undergoes an alpha decay, followed by a beta-minus decay. What is the number of protons and neutrons in the resulting nuclide?

What statement is not true about radioactive decay?

A.  The percentage of radioactive nuclei of an isotope in a sample of that isotope after 7 half-lives is smaller than 1 %.

B.  The half-life of a radioactive isotope is the time taken for half the nuclei in a sample of that isotope to decay.

C.  The whole-life of a radioactive isotope is the time taken for all the nuclei in a sample of that isotope to decay.

D.  The half-life of radioactive isotopes range between extremely short intervals to thousands of millions of years.

What statement is not true about radioactive decay?

A.  The percentage of radioactive nuclei of an isotope in a sample of that isotope after 7 half-lives is smaller than 1 %.

B.  The half-life of a radioactive isotope is the time taken for half the nuclei in a sample of that isotope to decay.

C.  The whole-life of a radioactive isotope is the time taken for all the nuclei in a sample of that isotope to decay.

D.  The half-life of radioactive isotopes range between extremely short intervals to thousands of millions of years.

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Estimate the fraction of tritium remaining after one year.

Estimate the fraction of tritium remaining after one year.

Estimate the fraction of tritium remaining after one year.

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Explain how the difference in part (b)(ii) arises.

Explain how the difference in part (b)(ii) arises.

Explain how the difference in part (b)(ii) arises.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.