DP Physics Questionbank

Determine the time taken for the foam to drop to

(i) half its initial height.

(ii) a quarter of its initial height.

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?

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.  $\frac{1}{4}$

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.

Write down the nuclear equation for this decay.

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.

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

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.

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.

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^–

write down the momentum of the neutrino.

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

Identify the missing information for this decay.

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

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.

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

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

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).

Explain your answer to (b).

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

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).

Explain your answer to (a)(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.

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

Write down the nuclear equation that represents this reaction.

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 diagram shows the emission spectrum of an atom.

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

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?

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

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.

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

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 proton number of nuclide X.

State the half-life of Sr-94.

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

Write down the proton number of nuclide X.

State the half-life of Sr-94.

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 equation to represent this 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.

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

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

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.

Write down the equation to represent this 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.

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

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.

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

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.

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

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

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.

When an alpha particle collides with a nucleus of nitrogen-14 $\left({}_7^{14}\mathrm{N}\right)$, a nucleus X can be produced together with a proton. What is X?

A. ${}_8^{18}\mathrm{X}$

B. ${}_8^{17}\mathrm{X}$

C. ${}_9^{18}\mathrm{X}$

D. ${}_9^{17}\mathrm{X}$

Carbon-14 (C-14) is a radioactive isotope which undergoes beta minus (β^–) decay to the stable isotope nitrogen-14 (N-14). Energy is released during this decay. Explain why the mass of a C-14 nucleus and the mass of a N-14 nucleus are slightly different even though they have the same nucleon number.

What is the definition of the unified atomic mass unit?

A.  $\frac{1}{12}$ the mass of a neutral atom of carbon-12

B.  The mass of a neutral atom of hydrogen-1

C.  $\frac{1}{12}$ the mass of a nucleus of carbon-12

D.  The mass of a nucleus of hydrogen-1

In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a nucleus of element Y and a nucleus of element Z.

X + n → Y + Z + 2n

What is $\frac{\text{magnitude of the binding energy per nucleon of Y}}{\text{magnitude of the binding energy per nucleon of X}}$ and $\frac{\text{total binding energy of Y and Z}}{\text{total binding energy of X}}$?

What is the energy equivalent to the mass of one proton?

A.  9.38 × (3 × 10⁸)² × 10⁶ J

B.  9.38 × (3 × 10⁸)² × 1.6 × 10^–19 J

C.  $\frac{9.38\times {10}^8}{1.6\times {10}^{-19}}$J

D.  9.38 × 10⁸ × 1.6 × 10^–19 J

The binding energy per nucleon of ${}_4^{11}Be$ is 6 MeV. What is the energy required to separate the nucleons of this nucleus?

A.  24 MeV

B.  42 MeV

C.  66 MeV

D.  90 MeV

In the nuclear reaction X + Y → Z + W, involving nuclides X, Y, Z and W, energy is released. Which is correct about the masses (M) and the binding energies (BE) of the nuclides?

The average binding energy per nucleon of the ${}_8^{15}\text{O}$ nucleus is 7.5 MeV. What is the total energy required to separate the nucleons of one nucleus of ${}_8^{15}\text{O}$?

A.     53 MeV

B.     60 MeV

C.     113 MeV

D.     173 MeV

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

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

Identify particle X.

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 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?

Calculate the binding energy per nucleon for uranium-238.

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

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.  $200 \mathrm{GW}$

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

Uranium-235 $\left({}_{92}{}^{235}\text{U}\right)$ is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.

Determine, in MeV and using the graph, the energy released by this fission.

During the nuclear fission of nucleus X into nucleus Y and nucleus Z, energy is released. The binding energies per nucleon of X, Y and Z are $B_{\text{X}}$ , $B_{\text{Y}}$ and $B_{\text{Z}}$ respectively. What is true about the binding energy per nucleon of X, Y and Z?

A.  $B_{\text{Y}}$ > $B_{\text{X}}$ and $B_{\text{Z}}$ > $B_{\text{X}}$

B.  $B_{\text{X}}$ = $B_{\text{Y}}$ and $B_{\text{X}}$ = $B_{\text{Z}}$

C.  $B_{\text{X}}$ > $B_{\text{Y}}$ and $B_{\text{X}}$ > $B_{\text{Z}}$

D.  $B_{\text{X}}$ = $B_{\text{Y}}$ + $B_{\text{Z}}$

Uranium-235 (${}_{92}{}^{235}\text{U}$) is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.

Determine, in MeV and using the graph, the energy released by this fission.

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

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

Show that the energy released in this decay is about 6 MeV.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

Show that the energy released in this decay is about 6 MeV.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

A neutron is absorbed by a nucleus of uranium-235$\left({}_{92}{}^{235}\text{U}\right)$. One possible outcome is the production of two nuclides, barium-144$\left({}_{56}{}^{144}\text{Ba}\right)$ and krypton-89$\left({}_{36}{}^{89}\text{Kr}\right)$.

How many neutrons are released in this reaction?

A.  0

B.  1

C.  2

D.  3

A particular K meson has a quark structure $\overline{\mathrm{u}}$s. State the charge on this meson.

A particular K meson has a quark structure $\overline{\mathrm{u}}$s. State the charge, strangeness and baryon number for this meson.

The Feynman diagram shows the changes that occur during beta minus (β^–) decay.

Label the diagram by inserting the four missing particle symbols and the direction of the arrows for the decay particles.

Draw arrow heads on the lines representing $\overline{u}$ and d in the ${\pi }^{-}$.

The reaction p⁺ + n⁰ → p⁺ + $\pi$⁰ does not occur because it violates the conservation law of

A.  electric charge.

B.  baryon number.

C.  lepton number.

D.  strangeness.

Which Feynman diagram shows beta-plus (β⁺) decay?

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

Draw a labelled arrow to complete the Feynman diagram.

Identify particle V.

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

The following interaction is proposed between a proton and a pion.

p⁺ + $\pi$^– → K^– + $\pi$⁺

The quark content of the $\pi$^– is ūd and the quark content of the K^– is ūs.

Three conservation rules are considered

I.   baryon number

II.  charge

III. strangeness.

Which conservation rules are violated in this interaction?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

The following decay is observed.

μ⁻ → e⁻ + v_μ + X

What is particle X?

A.   γ

B.   $\overline{v}$_e

C.   Z⁰

D.   v_e

Sketch the Feynman diagram that represents this reaction. The diagram has been started for you.

Energy is transferred to a hadron in an attempt to separate its quarks. Describe the implications of quark confinement for this situation.

The ${\pi }^{+}$ meson contains an up ($u$) quark. What is the quark structure of the ${\pi }^{-}$ meson?

A. $ud$

B. $u\overline{d}$

C. $\overline{u}d$

D. $\overline{u}\overline{d}$

Three conservation laws in nuclear reactions are

I. conservation of charge

II. conservation of baryon number

III. conservation of lepton number.

The reaction

$n\to {\pi }^{-}+e^{+}+{\overline{v}}_e$

is proposed.

Which conservation laws are violated in the proposed reaction?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

The Feynman diagram shows some of the changes in a proton–proton collision.

What is the equation for this collision?

A.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\mathrm{n}+{\mathrm{\pi }}^{+}$

B.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\mathrm{n}+{\mathrm{\pi }}^{-}$

C.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\overline{\mathrm{n}}+{\mathrm{\pi }}^{+}$

D.  $\mathrm{p}+\mathrm{p}\to \mathrm{p}+\overline{\mathrm{n}}+{\mathrm{\pi }}^{-}$

Thallium-206 $\left({}_{81}{}^{206}\text{Tl}\right)$ decays into lead-206 $\left({}_{82}{}^{206}\text{Pb}\right)$.

Identify the quark changes for this decay.

When a pi meson π- (du̅) and a proton (uud) collide, a possible outcome is a sigma baryon Σ⁰ (uds) and a kaon meson Κ⁰ (ds̅).

Apply three conservation laws to show that this interaction is possible.

The neutron number N and the proton number Z are not equal for the nuclide ${}_{81}{}^{205}\text{Tl}$. Explain, with reference to the forces acting within the nucleus, the reason for this.

A particle reaction is

$p+e^{-}+{\overline{V}}_{\mu }\to n+{\mu }^{+}+v_e$.

Which conservation law is violated by the reaction?

A. Baryon number

B. Charge

C. Lepton number

D. Momentum

Thallium-206 $\left({}_{81}{}^{206}\text{Tl}\right)$ decays into lead-206 $\left({}_{82}{}^{206}\text{Pb}\right)$.

Identify the quark changes for this decay.

The neutron number N and the proton number Z are not equal for the nuclide ${}_{81}{}^{205}\text{Tl}$. Explain, with reference to the forces acting within the nucleus, the reason for this.

Describe the quark structure of a baryon.