On the graph, sketch how the number of boron nuclei in the sample varies with time.

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

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?

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

The diagram shows atomic transitions E₁, E₂ and E₃ when a particular atom changes its energy state. The wavelengths of the photons that correspond to these transitions are ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$.

What is correct for these wavelengths?

A.  ${\lambda }_1>{\lambda }_2>{\lambda }_3$

B.  ${\lambda }_1={\lambda }_2+{\lambda }_3$

C.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2+{\lambda }_3}$

D.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$

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.  $\frac{8}{7}$

Two pure samples of radioactive nuclides X and Y have the same initial number of atoms. The half-life of X is $T_{\frac{1}{2}}$.

After a time equal to 4 half-lives of X the ratio $\frac{\text{number of atoms of X}}{\text{number of atoms of Y}}$ is $\frac{1}{8}$.

What is the half-life of Y?

A.     $0.25T_{\frac{1}{2}}$

B.     $0.5T_{\frac{1}{2}}$

C.     $3T_{\frac{1}{2}}$

D.     $4T_{\frac{1}{2}}$

Identify the missing information for this decay.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. State the number of remaining beryllium-10 nuclei in the sample after 2.8 × 10⁶ years.

Copper (${}_{29}^{64}\text{Cu}$) decays to nickel (${}_{28}^{64}\text{Ni}$). What are the particles emitted and the particle that mediates the interaction?

Explain your answer to (b).

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a)(i).

${}_{15}^{32}\text{P}$ 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.

Write down the nuclear equation for this decay.

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.

State the half-life of Sr-94.

Write down the proton number of nuclide X.

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.

Which of the following atomic energy level transitions corresponds to photons of the shortest wavelength?

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 pure sample of nuclide A and a pure sample of nuclide B have the same activity at time t = 0. Nuclide A has a half-life of T, nuclide B has a half-life of 2T.

What is $\frac{\text{activity of A}}{\text{activity of B}}$ when t = 4T?

A.  4

B.  2

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

Determine the time taken for the foam to drop to

(i) half its initial height.

(ii) a quarter of its initial height.

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

Rutherford and Royds identified the helium gas in cylinder B by observing its emission spectrum. Outline, with reference to atomic energy levels, how an emission spectrum is formed.

The diagram shows the emission spectrum of an atom.

Which of the following atomic energy level models can produce this spectrum?

On the graph, sketch how the number of boron nuclei in the sample varies with time.

A nucleus of phosphorus (P) decays to a nucleus of silicon (Si) with the emission of particle X and particle Y.

$${}_{15}^{30}\text{P}\to {}_{14}^{30}\text{Si}+\text{X}+\text{Y}$$

What are X and Y?

Element X decays through a series of alpha (α) and beta minus (β^–) emissions. Which series of emissions results in an isotope of X?

A.     1α and 2β^–

B.     1α and 4β^–

C.     2α and 2β^–

D.     2α and 3β^–

Identify, with an arrow labelled B on the diagram, the transition in the hydrogen spectrum that gives rise to the photon with the energy in (a).

Identify the missing information for this decay.

Explain your answer to (a)(ii).

Another radioactive source consists of a nuclide of caesium $\left({}_{55}{}^{137}\text{Cs}\right)$ that decays to barium $\left({}_{56}{}^{137}\text{Ba}\right)$.

Write down the reaction for this decay.

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

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

Four of the energy states for an atom are shown. Transition between any two states is possible.

What is the shortest wavelength of radiation that can be emitted from these four states?

A.  $\frac{hc}{E_4-E_1}$

B.  $\frac{hc}{E_4}-\frac{hc}{E_1}$

C.  $\frac{hc}{E_4-E_3}$

D.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

Write down the equation to represent this decay.

Calculate the mass of Sr-94 remaining in the sample after $10$ minutes.

Uranium-238 decays into a nuclide of thorium-234 (Th).

Write down the complete equation for this radioactive decay.

Write down the proton number of nuclide X.

State the half-life of Sr-94.

Thallium-205 (${}_{81}{}^{205}\text{Tl}$) can also form from successive alpha (α) and beta-minus (β⁻) decays of an unstable nuclide. The decays follow the sequence α β⁻ β⁻ α. The diagram shows the position of ${}_{81}{}^{205}\text{Tl}$ on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N and Z that occur as the ${}_{81}{}^{205}\text{Tl}$ forms from the unstable nuclide.

Write down the equation to represent this decay.

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?

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.  $\frac{A_0}{8}$

Uranium-238 decays into a nuclide of thorium-234 (Th).

Write down the complete equation for this radioactive decay.

Thallium-205 (${}_{81}{}^{205}\text{Tl}$) can also form from successive alpha (α) and beta-minus (β⁻) decays of an unstable nuclide. The decays follow the sequence α β⁻ β⁻ α. The diagram shows the position of ${}_{81}{}^{205}\text{Tl}$ on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N and Z that occur as the ${}_{81}{}^{205}\text{Tl}$ forms from the unstable nuclide.

Calculate the mass of Sr-94 remaining in the sample after $10$ minutes.

Determine the energy of a photon of blue light (435nm) emitted in the hydrogen spectrum.

The diagram below shows four energy levels for the atoms of a gas. The diagram is drawn to scale. The wavelengths of the photons emitted by the energy transitions between levels are shown.

What are the wavelengths of spectral lines, emitted by the gas, in order of decreasing frequency?

A.  ${\lambda }_3, {\lambda }_2, {\lambda }_1, {\lambda }_4$

B.  ${\lambda }_4, {\lambda }_1, {\lambda }_2, {\lambda }_3$

C.  ${\lambda }_4, {\lambda }_3, {\lambda }_2, {\lambda }_1$

D.  ${\lambda }_4, {\lambda }_2, {\lambda }_1, {\lambda }_3$

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

Suggest why the β^– decay is followed by the emission of a gamma ray photon.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

Write down the nuclear equation that represents this reaction.

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 ${}_0{}^0\overline{\text{v}}_{\text{e}}$

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

Carbon (C-12) and hydrogen (H-1) undergo nuclear fusion to form nitrogen.

${}_6{}^{12}\text{C+}{}_1{}^1\text{H →N+}$ photon

What is the number of neutrons and number of nucleons in the nitrogen nuclide?

Write down the equation for this decay.

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.