Electron capture can be represented by the equation

p + e^– → X + Y.

What are X and Y?

D

Pair production by a photon occurs in the presence of a nucleus. For this process, which of momentum and energy are conserved?

D

A radioactive element has decay constant $\lambda$ (expressed in s^–1). The number of nuclei of this element at t = 0 is N. What is the expected number of nuclei that will have decayed after 1 s?

A.  $N\left(1-e^{-\lambda }\right)$

B.  $\frac{N}{\lambda }$

C.  $N{e}^{-\lambda }$

D.  $\lambda N$

A

What can be used to calculate the probability of finding an electron in a particular region of space?

A.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in energy}}$

B.  $\frac{\text{Planck's constant}}{4\pi \times \text{uncertainty in speed}}$

C.  The magnitude of the wave function

D.  The magnitude of the (wave function)²

D

Monochromatic light is incident on a metal surface and electrons are released. The intensity of the incident light is increased. What changes, if any, occur to the rate of emission of electrons and to the kinetic energy of the emitted electrons?

D

Which of the following is evidence for the wave nature of the electron?

A.     Continuous energy spectrum in β^– decay

B.     Electron diffraction from crystals

C.     Existence of atomic energy levels

D.     Existence of nuclear energy levels

B

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

A photon interacts with a nearby nucleus to produce an electron. What is the name of this process?

A. Pair annihilation

B. Pair production

C. Electron diffraction

D. Quantum tunnelling

B

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

A

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.  $8{\rho }_{\text{X}}$

B

What was a reason to postulate the existence of neutrinos?

A. Nuclear energy levels had a continuous spectrum.

B. The photon emission spectrum only contained specific wavelengths.

C. Some particles were indistinguishable from their antiparticle.

D. The energy of emitted beta particles had a continuous spectrum.

D

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

D

When monochromatic light is incident on a metallic surface, electrons are emitted from the surface. The following changes are considered.

I.    Increase the intensity of the incident light
II.   Increase the frequency of light
III.  Decrease the work function of the surface

Which changes will result in electrons of greater energy being emitted from the surface?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

C

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

D

Monochromatic electromagnetic radiation is incident on a metal surface. The kinetic energy of the electrons released from the metal

A. is constant because the photons have a constant energy.

B. is constant because the metal has a constant work function.

C. varies because the electrons are not equally bound to the metal lattice.

D. varies because the work function of the metal is different for different electrons.

C

What is true for the Bohr model for the hydrogen atom?

A.  Angular momentum of electrons is quantized.

B.  Electrons are described by wave functions.

C.  Electrons never exist in fixed orbitals.

D.  Electrons will continuously emit radiation.

A

The diameter of a silver-108 (${}_{47}^{108}Ag$) nucleus is approximately three times that of the diameter of a nucleus of

A.  ${}_2^{4}He.$

B.  ${}_3^{7}Li.$

C.  ${}_5^{11}B.$

D.  ${}_{10}^{20}Ne.$

A

What is evidence for wave–particle duality?

A.  Line spectra of elements

B.  Electron-diffraction experiments

C.  Rutherford alpha-scattering experiments

D.  Gamma-ray spectra

B

This question was generally well answered by HL candidates.

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

C

Roughly half of candidates (incorrectly) selected response D, without recognizing that the change in activity over time is not linear.

What is a consequence of the uncertainty principle?

A. The absorption spectrum of hydrogen atoms is discrete.

B. Electrons in low energy states have short lifetimes.

C. Electrons cannot exist within nuclei.

D. Photons do not have momentum.

C

A particle of energy $E$ is incident upon a barrier and has a certain probability of quantum tunnelling through the barrier. Assuming $E$ remains constant, which combination of changes in particle mass and barrier length will increase the probability of the particle tunnelling through the barrier?

A

An electron of initial energy E tunnels through a potential barrier. What is the energy of the electron after tunnelling?

A.     greater than E

B.     E

C.     less than E

D.     zero

B

A particle is confined within a nucleus. What is the order of magnitude of the uncertainty in the momentum of the particle?

A. 10^–10 N s

B. 10^–15 N s

C. 10^–20 N s

D. 10^–25 N s

C

Response B was an effective distractor for over a third of candidates.

The size of a nucleus can be estimated from electron diffraction experiments. What is the order of magnitude of the de Broglie wavelength of the electrons in these experiments?

A.  10⁻¹⁵ m

B.  10⁻¹³ m

C.  10⁻¹¹ m

D.  10⁻⁹ m

A

A radioactive nuclide is known to have a very long half-life.

Three quantities known for a pure sample of the nuclide are

I.   the activity of the nuclide

II.  the number of nuclide atoms

III. the mass number of the nuclide.

What quantities are required to determine the half-life of the nuclide?

A.   I and II only

B.   I and III only

C.   II and III only

D.   I, II and III

A

A beam of electrons moving in the direction shown is incident on a rectangular slit of width $d$.

The component of momentum of the electrons in direction $y$ after passing through the slit is $p$. The uncertainty in $p$ is

A.  proportional to $d$

B.  proportional to $\frac{1}{d}$

C.  proportional to $\frac{1}{d^2}$

D.  zero

B

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.  $4$

A

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.

D

This question was well answered by HL candidates.

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

A

Options B and C were both effective distractors in this photoelectric effect question. There was a heightened number of blanks (no response) relative to the questions immediately before and after, and the low difficulty index suggests that candidates found this question challenging.

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

Which is the correct Feynman diagram for pair annihilation and pair production?

D

Three possible features of an atomic model are

I. orbital radius

II. quantized energy

III. quantized angular momentum.

Which of these are features of the Bohr model for hydrogen?

A. I and II only

B. I and III only

C. II and III only

D. I, II, and III

D

An electron of low energy is enclosed within a high potential barrier. What is the process by which the electron can escape?

A. Quantum tunneling

B. Energy–mass conversion

C. Diffraction

D. Barrier climbing

A

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.     $\frac{T}{4}$

C

The Rutherford-Geiger-Marsden experiment shows that

A.  alpha particles do not obey Coulomb’s law.

B.  there is a fixed nuclear radius for each nucleus.

C.  a large proportion of alpha particles are undeflected.

D.  the Bohr model of the hydrogen atom is confirmed.

C

This has a low discrimination index but it was felt that perhaps as it was the last question students were guessing the answer especially those choosing option A.

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

B

A particle of fixed energy is close to a potential barrier.

Which changes to the width of the barrier and to the height of the barrier will always make the tunnelling probability greater?

D

A neutron of mass m is confined within a nucleus of diameter d. Ignoring numerical constants, what is an approximate expression for the kinetic energy of the neutron?

A.  $\frac{h^2}{m{d}^2}$

B.  $\frac{h}{md}$

C.  $\frac{m{h}^2}{d^2}$

D.  $\frac{h}{m^{2}d}$

A

When green light is incident on a clean zinc plate no photoelectrons are emitted. What change may cause the emission of photoelectrons?

A.   Using a metal plate with larger work function

B.   Changing the angle of incidence of the green light on the zinc plate

C.   Using shorter wavelength radiation

D.   Increasing the intensity of the green light

C

According to the Bohr model for hydrogen, visible light is emitted when electrons make transitions from excited states down to the state with n = 2. The dotted line in the following diagram represents the transition from n = 3 to n = 2 in the spectrum of hydrogen.

Which of the following diagrams could represent the visible light emission spectrum of hydrogen?

B

Alpha particles with energy E are directed at nuclei with atomic number Z. Small deviations from the predictions of the Rutherford scattering model are observed.

Which change in E and which change in Z is most likely to result in greater deviations from the Rutherford scattering model?

B

Which graph shows a possible probability density function ${\left|\text{Ψ}\right|}^2=\frac{P\left(r\right)}{\Delta V}$ for a given wave function $\text{Ψ}$ of an electron?

C

An electron of non-relativistic speed $v$ interacts with an atom. All the energy of the electron is transferred to an emitted photon of frequency $f$ . An electron of speed $2v$ now interacts with the same atom and all its energy is transmitted to a second photon. What is the frequency of the second photon?

A.  $\frac{f}{4}$

B.  $\frac{f}{2}$

C.  $2f$

D.  $4f$

D

A photoelectric cell is connected in series with a battery of emf 2 V. Photons of energy 6 eV are incident on the cathode of the photoelectric cell. The work function of the surface of the cathode is 3 eV.

What is the maximum kinetic energy of the photoelectrons that reach the anode?

A.     1 eV

B.     3 eV

C.     5 eV

D.     8 eV

A

A proton has momentum 10^-20 N s and the uncertainty in the position of the proton is 10^-10 m. What is the minimum fractional uncertainty in the momentum of this proton?

A. 5 × 10^-25

B. 5 × 10^-15

C. 5 × 10^-5

D. 2 × 10⁴

C

Over 100 candidates left this blank. It is testing fractional uncertainty and also involves the Heisenberg uncertainty principle.

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

D

Photons of discrete energy are emitted during gamma decay. This is evidence for

A. atomic energy levels.

B. nuclear energy levels.

C. pair annihilation.

D. quantum tunneling.

B

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

D

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

B

A low discrimination index with the majority of candidates choosing option D when B is correct. Students tend to link the intensity of light to the number of photons but forget that it is the energy (per unit time per unit area) of the light so if the photon energy increases (frequency increases) then the number of photons must decrease.

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

A

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

A photon of energy E and wavelength λ is scattered from an electron initially at rest.

What is the energy of the photon and the wavelength of the photon when the electron moves away?

D

Three observations of the behaviour of electrons are

I.   electron emission as a result of the photoelectric effect
II.  electron diffraction as an electron interacts with an atom
III. emission of radio waves as a result of electrons oscillating in a conductor.

Which observations are evidence that the electron behaves as a particle?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

B

A metallic surface is first irradiated with infrared radiation and photoelectrons are emitted from the surface. The infrared radiation is replaced by ultraviolet radiation of the same intensity.

What will be the change in the kinetic energy of the photoelectrons and the rate at which they are ejected?

A

With a low difficulty index, fewer than 15 % of candidates correctly selected response A. The large majority of candidates selected response C. These candidates likely did not recognize that since intensity stays constant, there must be fewer ultraviolet photons ejected for the power per unit area to remain constant. The discrimination index was very low for this question.

Three correct statements about the behaviour of electrons are:

I.   An electron beam is used to investigate the structure of crystals.
II.  An electron beam produces a pattern of fringes when sent through two narrow parallel slits.
III. Electromagnetic radiation ejects electrons from the surface of a metal. 

Which statements are explained using the wave-like properties of electrons?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A

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.  $155$

C

An electron of mass m has an uncertainty in its position r. What is the uncertainty in the speed of this electron?

A. $\frac{h}{4\pi r}$

B. $\frac{hr}{4\pi m}$

C. $\frac{hm}{4\pi r}$

D. $\frac{h}{4\pi mr}$

D

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

C

In the Bohr model for hydrogen an electron in the ground state has orbit radius r and speed v. In the first excited state the electron has orbit radius 4r. What is the speed of the electron in the first excited state?

A.  $\frac{v}{2}$

B.  $\frac{v}{4}$

C.  $\frac{v}{8}$

D.  $\frac{v}{16}$

A

Which of the following, observed during a radioactive-decay experiment, provide evidence for the existence of nuclear energy levels?

I.   The spectrum of alpha particle energies
II.  The spectrum of beta particle energies 
III. The spectrum of gamma ray energies 

A. I and II only

B. I and III only 

C. II and III only 

D. I, II and III

B