IBPhysicsHLTopic QuestionsNuclear & Quantum PhysicsStructure of the Atom

Syllabus Edition

First teaching 2023

First exams 2025

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Structure of the Atom (HL IB Physics)

Topic Questions

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1a
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Match, by drawing a line, the words with their correct definitions.

7-1-q1a-question--sl-sq-easy-phy

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1b
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The energy of a photon can be calculated using the equation

E equals fraction numerator h c over denominator lambda end fraction

Define the following terms and give the unit:

 

(i)
h
[2]
(ii)
c
[2]
(iii)
λ
[2]

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1c
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Calculate the wavelength of a photon with an energy of 1.44 × 10−19 J.

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1d
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(i)
Complete the gaps in the following paragraph by writing the correct words on the line.

 

Electrons in an atom can only have specific energies. These energies are called _________ _________ _______ .

Normally, electrons occupy the _______ energy level available. This is known as the __________ __________.

Electrons can gain energy and move up the energy levels by ______________  energy. 
[4]

 

(ii)
Underline the processes that allow an electron to move up an energy level.

Collisions with other atoms or electrons      Releasing a photon       Radioactive decay      Absorbing a photon   Changing colour      Emitting a neutrino      

A physical source, such as heat

[3]

   

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2a
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In a hydrogen atom, an electron of mass m orbits the proton with speed v in a circular orbit of radius r.

The diagram shows an electron wave in hydrogen.

electron-wave-hydrogen

 

(i)
State the meaning of the term electron wave.
[1]

(ii)
Identify the number of allowed electron orbits shown in the diagram.
[1]

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2b
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By equating the centripetal and electric forces acting on the electron, show that the speed v of an electron in the hydrogen atom is related to the radius r of its orbit by the expression

 
v space equals space square root of fraction numerator k e squared over denominator m subscript e r end fraction end root

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2c
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Using your answer to (b) and the Bohr condition, deduce that the radius r of the electron’s orbit in the n level of hydrogen is given by the following expression:

r space equals space fraction numerator n squared h squared over denominator 4 straight pi squared k m subscript e e squared end fraction

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2d
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Calculate the electron’s maximum orbital radius, r.

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3a
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Outline how the density of a nucleus varies with nuclear radius.

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3b
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Calculate the nuclear radius of carbon-14 open parentheses straight C presubscript 6 presuperscript 14 close parentheses, in m.

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3c
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Carbon-14 is unstable and decays to nitrogen by beta minus emission.

In living tissue, such as plants and animals, the ratio of carbon-14 to carbon-12 atoms is constant.

State and explain what will happen to this ratio after the living tissue dies.

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4a
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A beam of electrons each of de Broglie wavelength 2.8 × 10–15 m is incident on a thin film of iron-56 open parentheses F presubscript 26 presuperscript 56 italic e close parentheses. The variation in the electron intensity of the beam with scattering angle is shown.

electron-scattering-graph

Use the graph to determine the nuclear radius of iron-56.

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4b
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Using the result from part (a):

(i)
Show that the constant of proportionality, R0, is equal to 1.2 fm
[2]
(ii)
Calculate the nuclear radius of radium-222 open parentheses R presubscript 88 presuperscript 222 a close parentheses
[1]

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4c
Sme Calculator2 marks

Two students debate whether beams of electrons or alpha particles, of the same energy, would be better for investigating the size of a nucleus. 

Complete the sentences below to outline which student is correct.

Beams of ____________ would be better for investigating the size of a nucleus.

This is because a beam of ____________ would provide a greater resolution since their de Broglie wavelength is _________ than the de Broglie wavelength of ____________.

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4d
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The graph shows how the number of alpha particles that are observed at a fixed scattering angle, N, depends on alpha particle energy, E, according to Rutherford’s scattering formula.

rutherford-deviations

Deviations from Rutherford scattering are detected in experiments carried out at high energies.

 
(i)
Outline an assumption of the Rutherford scattering formula.
[1]
(ii)
Indicate the deviations from Rutherford scattering on the axes provided above. 
[1]
(iii)
Explain what these deviations provide evidence for.
[3]

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5a
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Particles can be used in scattering experiments to estimate nuclear radius.

Outline how these experiments are carried out by completing the following sentences: 

High ______________ particles have wave-like properties such as a ____________ wavelength and the ability to ____________ when incident on a thin _______________.

The ____________ of the _______________ particles can be measured using a detector.

A graph of intensity against _______________ can be obtained.

The ________________ of the first _____________ can be used to determine the nuclear radius of the atoms in the _________________.

The nuclear radius can then be determined using the equation ____________________.

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5b
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Electron scattering experiments indicate that the nuclear radius of oxygen-16 is 3.02 fm

The graph shows the variation of nuclear radius with nucleon number. The nuclear radius of the oxygen-16 has been plotted.

nuclear-radius-graph

Plot the position of sulphur-32 on the graph. 

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5c
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The density of a nucleus, ρ, is given by the equation:

rho space equals space fraction numerator 3 u over denominator 4 straight pi R subscript italic 0 to the power of italic 3 end fraction

Where u is the atomic mass unit and R0 is a constant of proportionality equal to approximately 1.20 × 10–15 m.

(i)
State how the density of a nucleus changes after it undergoes radioactive decay.
[1]
(ii)
Explain your answer to part (i).
[1]

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5d
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Draw a line on the graph to show how nuclear radius varies with nucleon number.

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1a
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Transitions between three energy levels in a particular atom give rise to three spectral lines. In decreasing magnitudes, these are f subscript 1, f subscript 2and f subscript 3.

The equation which relates f subscript 1, f subscript 2 and f subscript 3 is:

f subscript 1 equals f subscript 2 plus f subscript 3

Explain, including through the use of a sketch, how this equation relates f subscript 1, f subscript 2 and f subscript 3.

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1b
Sme Calculator5 marks

A different atom has a complete line emission spectra with a ground state energy of  –10.0 eV. is:

7-1-ib-sl-hard-sqs-q1b-question

Sketch and label a diagram of the possible energy levels for the atomic line spectra shown.

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1c
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Explain the significance of an electron at an energy level of 0 eV.

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1d
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(i)
Explain the statement 'the first excitation energy of the hydrogen atom is 10.2 eV'
  [1]
(ii)
The ground state of hydrogen is –13.6 eV. Calculate the speed of the slowest electron that could cause this excitation of a hydrogen atom. 
[2]

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2a
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Bohr modified the Rutherford model by introducing the condition: 

m v r space equals space n fraction numerator h over denominator 2 straight pi end fraction. 

The total energy En of an electron in a stable orbit is given by:

E subscript n equals negative fraction numerator k e squared over denominator 2 r end fraction

Where k equals fraction numerator 1 over denominator 4 straight pi epsilon subscript 0 end fraction

(i)
Discuss one issue posed by Rutherford's model and one issue solved by Bohr's modification. 
[2]
(ii)
Use Bohr's modification with the expression for total energy to derive the equation
  

E subscript n equals K over n squared

[3]

(iii)
State and explain what physical quantity is represented by the constant, K
[1]

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2b
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In 1908, the physicist Friedrich Paschen first observed the photon emissions resulting from transitions from a level n to the level n = 3 of hydrogen and deduced their wavelengths were given by:

lambda space equals space fraction numerator A n squared over denominator n squared space minus space 9 end fraction

where A is a constant.

Justify this formula on the basis of the Bohr theory for hydrogen and determine an expression for the constant A.

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3a
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In a scattering experiment, a metal foil of thickness 0.4 µm scatters 1 in 20 000 alpha particles through an angle greater than 90°.

(i)
Considering the metal foil as a number of layers of atoms, n, explain why the probability of an alpha particle being deflected by a given atom is approximately equal to
 
fraction numerator 1 over denominator 20 space 000 n end fraction
[2]
(ii)
Estimate the diameter of the nucleus. Consider the nuclei as cubes and the atoms in the foil as cubes of side length 0.25 nm.
[3]

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3b
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Deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.

Outline the incorrect assumption used in the Rutherford scattering formula and suggest an explanation for the observed deviations.

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3c
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In a scattering experiment, alpha particles were directed at five different thin metallic foils, as shown in the table.

 

Metal Symbol
Silver Ag presubscript 47 presuperscript 108
Aluminium Al presubscript 13 presuperscript 27
Gold Au presubscript 79 presuperscript 197
Tin Sn presubscript 50 presuperscript 119
Tungsten straight W presubscript 74 presuperscript 184

 

Initially, all alpha particles have the same energy. This energy is gradually increased. 

Predict and explain the differences in deviations from Rutherford scattering that will be observed.

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3d
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Outline why the particles must be accelerated to high energies in scattering experiments. 

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4a
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An electron beam of energy 1.3 × 10−10 J is used to study the nuclear radius of beryllium-9. The beam is directed from the left at a thin sample of beryllium-9. A detector is placed at an angle θ relative to the direction of the incident beam.

12-1-ib-hl-sqs-easy-q1b-question

The radius of a beryllium-9 nucleus is 2.9 × 10−15 m. The beryllium-9 nuclei behave like a diffraction grating. 

Sketch the expected variation of electron intensity against the angle from the horizontal.

Ie7rQUck_q3b

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4b
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The isotope beryllium-10 is formed when a nucleus of deuterium open parentheses straight H presubscript 1 presuperscript 2 close parentheses collides with a nucleus of beryllium-9 open parentheses Be presubscript 4 presuperscript 9 close parentheses. The radius of a deuterium nucleus is 1.5 fm.

 
(i)
Determine the minimum initial kinetic energy, in J, that the deuterium nucleus must have in order to produce the isotope beryllium-10.
[2]
(ii)
Outline an assumption made in this calculation.

[1]

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4c
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The nucleus of beryllium-9 is replaced by a nucleus of gold-197.

Suggest the change, if any, to the following: 

(i)
Distance of closest approach of a deuterium nucleus.
[2]
(ii)
Angle of minimum intensity from electron scattering. Assume the electrons have the same energy as in part (a).
[2]

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5a
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Show that all nuclei have the same density.

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5b
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A beam of neutrons is fired normally at a thin foil sheet made from tin. The beam has an energy of 75 MeV and the first diffraction minimum is observed at an angle of 15° relative to the central bright fringe.

Calculate an estimate for the radius of the tin nucleus.

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5c
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The tin open parentheses Sn presubscript 50 presuperscript 119 close parentheses foil is replaced by thin aluminium open parentheses Al presubscript 13 presuperscript 27 close parentheses foil.

Deduce and explain the expected difference in the observations between the two experiments.

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5d
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An isotope of tin has a half-life of 129 days. It undergoes beta-minus decay to a meta-stable isotope of antimony.

Calculate the percentage of the sample which will consist of antimony after 2 years.

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1a
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In a HeNe laser, electrons collide with helium atoms. The ground state of a helium is labelled as 1s and the next energy level is labelled 2s.

When an electrons de-excite from 2s to 1s in helium, photons are emitted with a wavelength of 58.4 nm.

Calculate the energy difference of this transition, giving your answer in eV.

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1b
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An electron collides with a helium in its ground state, causing an electron to transition from 1s to 2s. The electron initially has 45.0 eV of kinetic energy.

Calculate the electron’s kinetic energy after the collision.

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1c
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Explain why it is not possible for the same electron from (b) to collide with the ground state helium atom and be left with 40.0 eV of kinetic energy. 

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1d
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Helium and neon coincidentally have very similar energy gaps for certain transitions, allowing one atom to cause an excitation in the other.

The excited helium atom from part (b) then collides with a ground state neon atom. The neon atom becomes excited and subsequently emits two photons in order to return to its ground state.

(i)
If the helium is left back in its ground state after the collision, determine the amount of energy transferred to the neon atom.
[1]
(ii)
If one photon has an energy of 1.96 eV, calculate the wavelength of the other.
[4]

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2a
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Rutherford used the scattering of α particles to provide evidence for the structure of the atom. The apparatus includes a narrow beam of α particles fired at a very thin sheet of gold foil inside a vacuum chamber.

Explain why it is essential to use:

(i)
a vacuum in the chamber

[1]

(ii)
a very thin sheet of gold foil    

[1]

(iii)
a narrow beam of alpha particles   

[1]

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2b
Sme Calculator3 marks

The diagram shows α particles incident on a layer of atoms in a gold foil.

On the diagram, draw and complete the paths followed by each of the α particles shown.

ma1b_7-3_medium_ib-physics

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2c
Sme Calculator5 marks

Outline the results of the scattering experiment by explaining:

(i)
the main observations of the scattering experiment

[2]

(ii)
the significance of each observation

[3]

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2d
Sme Calculator6 marks

The Thomson model of the atom preceded Rutherford’s model. In the Thomson model, the atom was imagined as a sphere of positive charge of diameter 10–10 m containing electrons moving within the sphere.

Thomson’s model could explain some of the results of the Rutherford experiment, but not all.

Explain

(i)
why, at small deflections, Rutherford’s experiment can be explained by Thomson’s model but not at large deflections

[3]

(ii)
why Rutherford’s model of the atom can account for the results at both small and large deflections

[3]

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3a
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In the Rutherford scattering experiment, alpha particles are fired at a thin gold foil target using the experimental setup shown below.

12-2-hl-sqs-medium-q3a-question

Some of the alpha particles are backscattered.

Outline how the results of the Rutherford scattering experiment can be used to estimate the radius of a gold nucleus. Include a relevant equation.

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3b
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An alpha particle with an initial speed one-tenth that of the speed of light is fired head-on at a stationary gold nucleus open parentheses Au presubscript 79 presuperscript 197 close parentheses.

Calculate the minimum separation between the alpha particle and the centre of the gold nucleus.

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3c
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Estimate the number of nucleons in a gold nucleus based on the value of separation that you calculated in (b).

Comment on your answer in relation to:

  • the actual size of a gold nucleus
  • the accuracy of the Rutherford scattering method for determining nuclear radii.

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3d
Sme Calculator3 marks

The target nucleus is changed to one that has fewer protons. The alpha particle is fired with the same speed as before. 

Explain, without further calculation, the effect this has on the minimum separation.

Ignore any recoil effects.

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4a
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The Bohr model was developed in order to explain the atomic spectrum of hydrogen.

Outline the Bohr model and give a limitation of it.

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4b
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The Bohr model for hydrogen can also be applied to a helium atom which has lost one of its electrons through ionisation.

The one remaining electron has a mass of m and moves in a circular orbit of radius r. Deduce an expression for

(i)
the kinetic energy E subscript k of the electron
[2]
(ii)
the electric potential energy E subscript p
[1]
(iii)
the total energy E subscript T of the atom
[1]

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4c
Sme Calculator2 marks

Using your answer to (b), describe the predicted effect on the orbital radius of the electron when it

(i)
absorbs an electromagnetic wave
[1]
(ii)
emits an electromagnetic wave.
[1]

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4d
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The radius of the electron's orbit in the helium atom is 2.43 × 10−10 m.

Determine the principal quantum number of the energy level occupied by the electron.

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