Atomic Structure (Edexcel GCSE Chemistry): Exam Questions

4 hours31 questions
1a1 mark

The model of the atom has changed over time due to the discovery of the different subatomic particles.

Which subatomic particles led to J.J. Thomson's plum pudding model?

  • protons

  • neutrons

  • electrons

  • nucleus

1b1 mark

The diagram shows the structure of an atom using the current model of the atom.

screen-shot-2022-10-10-at-10-27-37

How does this diagram show that this is an atom of lithium?

  • it has three electrons

  • it has three protons

  • it has three protons and two neutrons

  • it has two neutrons

1c1 mark

Complete the sentence about atoms.

The size of the nucleus is very ................................ in comparison with the overall size of an atom.

1d1 mark

Which of these statements is correct about atoms?

  • electrons are positively charged

  • the number of protons is equal to the number of neutrons

  • most of the mass of an atom is concentrated in the nucleus

  • electrons are found in the nucleus

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2a3 marks

The diagram shows the particles in an atom of an element.

2c-q1

The box gives the names of some particles. 

2c-q1-1

Use words from the box to label the diagram.

2b1 mark

The table below shows three definitions of mass number.

Put a tick (✔) in the box to show which definition is the correct definition.

 The sum of the number of protons and electrons in the nucleus of an atom

 

 The number of protons in the nucleus of an atoms

 

 The sum of the number of protons and neutrons in the nucleus of an atom

 

2c1 mark

Give the mass number of the atom given in part a).

2d2 marks

Complete the sentence about isotopes.

Isotopes are atoms that have the same number of ........................................ but have a different number of .......................................... .

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3a1 mark

Atoms are made up of subatomic particles.

Which statement about subatomic particles is true?

  • Neutrons and electrons are found in the nucleus. Protons are found in shells

  • Protons and neutrons are found in the nucleus. Electrons are found in shells

  • Protons and electrons are found in the nucleus. Neutrons are found in shells

  • Neutrons are found in the nucleus. Protons and electrons are found in shells

3b1 mark

The table below shows three definitions of atomic number.

Put a tick ()  next to the correct definition. 

The number of electrons in the nucleus of an atom

 

The number of protons in the nucleus of an atom

 

The sum of the number of protons and neutrons in the nucleus of an atom

 

 

3c1 mark

The table below shows four descriptions of the distribution of electrons in an atom.

Put a tick ()  in the box to show which is the correct description. 

Electrons are evenly spread throughout the nucleus

 

Electrons are found only in the outermost shell

 

Electrons are concentrated in the nucleus

 

Electrons orbit the nucleus in specific energy levels or shells

 

 

3d3 marks

Use the words from the box to complete the sentences about the description of subatomic particles. 

shell                         1                              +1                               -1                              0             

 

Protons have a relative charge of _________ and a relative mass of _________. Neutrons have a relative charge of ___________. Electrons are found in shells and have a relative charge of -1.

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4a2 marks

Figure 1 shows some statements about the nucleus of an atom.

Put ticks () in the boxes in Figure 1 to show which statements are true and which statements are false 

 

True

False

The nucleus is very small compared to the overall size of an atom

 

 

The nucleus is larger than the atom

 

 

The nucleus is about the same size as the atom

 

 

The nucleus occupies majority of the mass of an atom

 

 

Figure 1

4b2 marks

The model of an atom has changed over time due to the development in experimental techniques.

Place ticks in boxes by the two statements which best describe what the gold foil experiment revealed about the structure of the atom. 

Figure 2

The nucleus is positively charged

 

Electrons are evenly distributed throughout the atom

 

The nucleus is small and contains most of the atom’s mass

 

Protons and neutrons are evenly distributed

 

4c1 mark

The diagram shows the structure of an atom using the current model of the atom.

edx-1-1e-q4c-dot-and-cross-diagram

How does this diagram show that this is an atom of beryllium?

  • It has 9 electrons

  • It has 9 protons

  • It has 4 protons

  • It has 5 neutrons

4d2 marks

The relative mass of carbon-12 is 12 and the relative mass of carbon-13 is 13.

Complete the following table about the subatomic particles found in two isotopes of carbon.

 

 

Number of protons

Number of neutrons

Number of electrons

 carbon-12

 6

 …………….

 6

 carbon-13

 6

 …………….

 6

 

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5a1 mark

Atoms have no charge overall.

Put a tick () next to the correct statement that describes why atoms have no overall charge. 

Atoms have the same number of protons and neutrons

 

Atoms have the same number of protons and electrons

 

Atoms have the same number of neutrons and electrons

 

5b4 marks

Use the words from the box to complete the sentences about the description of the structure of an atom. 

positively           negatively               neutrons              protons          magnetic       electrostatic 

 

The nucleus is ___________ charged due the presence of __________. There is _____________   attraction between the nucleus and ___________ charged electrons orbiting around the nucleus. This is what keeps an atom together.

5c1 mark

Atoms are made up of subatomic particles.

Which statement about the nucleus is true?

  • The nucleus has negligible mass

  • The nucleus contains protons and electrons

  • The mass of an atom is concentrated in the nucleus because it contains protons and electrons

  • The mass of an atom is concentrated in the nucleus because it contains protons and neutrons

5d1 mark

The diagram shows the structure of a beryllium atom using the current model of the atom.

edx-1-1-easy-paper-1-q5d

What is the nucleon number of this atom of beryllium? 

  • 14

  • 9

  • 8

  • 5

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6a1 mark

The diagram shows the particles in the atom of an element.

be-electronic-structure

Particle Y is a proton.

What is particle Z?

  • an electron

  • a molecul

  • a neutron

  • a nucleus

6b1 mark

Which of these has the smallest mass?

  • an electron

  • a neutron

  • a nucleus

  • a proton

6c1 mark

What is the mass number of this atom?

  • 4

  • 5

  • 9

  • 13

6d1 mark

What is the atomic number of this atom?

  • 4

  • 5

  • 9

  • 13

6e2 marks

i) Identify the element that contains this atom.

(1)

ii) State what is formed when this atom loses its outer shell electrons.

(1)

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7a1 mark

Two different atoms have a different number of neutrons.

The table below shows three statements about the two atoms.

Put a tick (✔) in the box to show which is the correct statement.

 The atoms are isotopes 

 

 The atoms must be different elements as they have a different number of neutrons

 

 The atoms could be the same element if they also had the same number of protons

 

 The atoms could be the same element if they also had the same number of electrons

 

7b1 mark

The relative atomic mass of chlorine is 35.5. Which is the correct reason why it is not a whole number?

  • chlorine contains half a proton

  • relative atomic mass is the average mass of all of the isotopes of that element

  • relative atomic mass is calculated from the mass of the protons divided by the mass of the neutrons

  • a chlorine molecule has a relative atomic mass of 71, so each atom has a relative atomic mass of 35.5

7c3 marks

Use words from the box to complete the sentences about chlorine.

protons

atomic

mass

neutrons

relative atomic

35-chlorine has the ................................ number of 35 and the ................................ number of 17. One atom of chlorine has 17 ................................ and electrons.

7d2 marks

The radius of a nucleus is approximately 10 000 times smaller than the radius of an atom.

Place ticks (✔) in boxes by the two statements about the atom that are correct.

 the mass of an atom is concentrated within the nucleus

 

 most of the space of an atom is filled with electrons

 

 most of an atom is empty space

 

 the mass of an atom is evenly distributed throughout the atoms

 

 most of the charge of an atom is concentrated in the nucleus

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8a1 mark

Use the words from the box to complete the sentences about the description of isotopes.  

neutrons                     protons                      compound                    element                        metal

Isotopes are atoms of the same __________ that contain the same number of __________ and electrons but a different number of ____________.

8b2 marks

Figure 1 shows some statements about the isotopes of carbon-12 (12C) and carbon-13 (13C). 

Put ticks () in the boxes in Figure 1 to show which statements are true and which statements are false 

 

True

False

Both carbon-12 and carbon-13 have the same number of protons

 

 

Carbon-12 has one less electron than carbon-13

 

 

Carbon-12 has one less neutron than carbon-13

 

 

Both carbon-12 and carbon-13 have the same number of neutrons

 

 

Figure 1

8c1 mark

Isotopes display the same chemical properties.

Put a tick () next to the correct statement that describes why isotopes display the same chemical properties.

Isotopes have the same number of neutrons in the nucleus

 

Isotopes have the same number of protons in the nucleus

 

Isotopes have the same number of electrons in their outer shells.

 

8d1 mark

J.J. Thomson discovered the electron and proposed a model of the atom known as the “plum pudding” model.

Which statement about the plum pudding model is true?

  • Negative electrons were located in the middle of a spherical cloud of positive charge

  • Negative electrons were spread around the edge of a spherical cloud of positive charge

  • Negative electrons were spread throughout the spherical cloud of positive charge

  • Positive charge was located in the middle of a sphere of negative charge

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9a3 marks

Use the words from the box to complete the sentences about Rutherford’s model of the atom. 

empty                     protons                  electrons                  full              concentrated                 little

 

Rutherford’s model of the atom was made up of mainly _________ space. The nucleus at the centre of the atom had ____________ mass, with ________ orbiting around the nucleus.

9b1 mark

The diagram shows the chemical symbol for lithium.

begin mathsize 36px style Li subscript 3 superscript 7 end style

Put two ticks () next to the correct statements that describe the lithium atom. 

The mass number is 3

 

The mass number is 7

 

The atomic number is 3

 

The atomic number is 7

 

9c1 mark

Hydrogen has three isotopes as shown in the diagram below.

straight H subscript 1 superscript 1

straight H subscript 1 superscript 2

straight H subscript 1 superscript 3

 Put a tick ()  in the box to show which statement best describes these isotopes. 

All the isotopes have 1 proton

 

All the isotopes have 1 neutrons

 

One of these isotopes has 3 neutrons

 

One of these isotopes has 2 electrons

 

9d1 mark

Which statement about finding the number of neutrons in an atom is true? 

  • Number of neutrons = mass number + atomic number

  • Number of neutrons = mass number + atomic number

  • Number of neutrons = mass number x atomic number

  • Number of neutrons = mass number x atomic number

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10a1 mark

Atomic models developed as scientists gained more experimental evidence.

Put a tick () next to the correct statement that describes one advancement in J.J. Thomson’s plum pudding model compared to Dalton’s model.  

Plum pudding model showed electrons orbiting in shells

 

Plum pudding model depicted electrons spread throughout a sphere of positive charge

 

Plum pudding model showed the atom with a nucleus in the center

 

10b1 mark

Rutherford’s gold foil experiment involved shooting a beam of positively charged particles at  gold foil.

Some positively charged particles deflected directly back.

What conclusion could be made from this observation? 

  • The atom is mainly empty space

  • There are negatively charged electrons orbiting the nucleus

  • There is a concentrated mass of positive charge at the centre of the atom

  • There is an abundance of negative charge at the centre of the atom

10c1 mark

There are two atoms with the same number of protons but a different number of neutrons.

Which statement about these atoms is true? 

  • The mass number of both atoms is the same

  • The atomic number of both atoms is different

  • The atomic and mass number of both atoms is the same

  • The atomic number is the same but the mass number is not the same

10d1 mark

The table below shows four statements about electrons.

Put a tick ()  next to the correct statement. 

Electrons have a mass of 1 and charge of -1

 

Electrons have a mass of 0 and charge of +1

 

Electrons have a mass of 0 and charge of -1

 

Electrons have a mass of 1 and charge of 0

 

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1
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1 mark

The atomic structure of an unknown element is shown below. 

1-1_q1-edexcel-gcse-mcq

What is the atomic number and mass number for the unknown element?

  • Atomic Number:6
    Mass Number: 11

  • Atomic Number:5
    Mass Number: 11

  • Atomic Number:5
    Mass Number: 6

  • Atomic Number:6
    Mass Number: 10

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2a3 marks

Atoms contain electrons, neutrons and protons.

i) Draw one line to link each particle to its correct relative charge. (2)


fig-q3ai-1cho-1f-paper-1-june-2018

ii) Which of the following is the relative mass of a proton?

(1)


A 0
B 1 over 1837
C
D -1

2b1 mark

Argon is in group 0 of the periodic table. Identify, using the periodic table, which of these elements is in the same period as argon.

  • bromine

  • iron 

  • magnesium 

  • xenon 

2c3 marks

Figure 4 shows the atomic number and mass number of two isotopes of argon.

isotope

atomic number

mass number

argon-38

18

38

argon-40

18

40

Figure 4

Describe the structure of an atom of argon-38 and of an atom of argon-40.

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31 mark

As the atomic model developed, protons, neutrons and electrons were discovered. 

What was the correct order of discovery?

  • Proton-Neutron-Electron

  • Proton-Electron-Neutron

  • Electron-Proton-Neutron

  • Electron-Neutron-Proton

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4a3 marks

Chlorine has an atomic number of 17.

Figure 3 shows the arrangement of electrons in an atom of chlorine.

fig-3-q2a-1cho-1f-paper-1-nov-2020

Figure 3

i) What is the electronic configuration of this atom?

(1)

A

10.7

B

17 

C

2.8.7 

D

7.8.2 

ii) Explain, using Figure 3, why chlorine belongs to group 7 of the periodic table.

(2)

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5 marks

The nucleus of an atom is made up of protons and neutrons. Atoms of chlorine contain 17 protons.

Figure 4 shows some information about a proton, a neutron and an electron.

 

relative mass

relative charge

proton

1

+1

neutron

1

0

electron

very small

 -1

Figure 4

i) Explain, using the information in Figure 3 and Figure 4, why atoms of chlorine have no overall charge.

(2)

ii) Atoms of chlorine-37 have a mass number of 37. Calculate the number of neutrons in atoms of chlorine-37.

(1)

number of neutrons = .................................................

iii) There are two isotopes of chlorine, chlorine-35 and chlorine-37. Explain the meaning of the term isotopes.

(2)

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51 mark

Chlorine–35 and chlorine–37 are isotopes. 

Which statement describes an isotope?

  • Atoms with the same number of protons and different numbers of electrons

  • Atoms with the same number of neutrons and different numbers of electrons

  • Atoms with the same number of protons and different numbers of neutrons

  • Atoms with the same number of neutrons and different numbers of protons

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6a
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3 marks

Higher Tier Only 

Titanium and iron are examples of transition metals.

Figure 6 shows the percentage abundance of each isotope in a sample of titanium.

fig-6-q6a-1cho-1h-paper-1-nov-2020

Figure 6

Calculate the relative atomic mass of titanium in this sample.

relative atomic mass = ......................................

6b4 marks

Iron, when heated in air, reacts with oxygen to form iron oxide.

i) This reaction is an example of (1)

A

crystallisation

B

distillation 

C

neutralisation 

D

oxidation 

ii) The equipment shown in Figure 7 can be used to find the mass of oxygen that combines with iron.

fig-7-q6bii-1cho-1h-paper-1-nov-2020

Figure 7

Describe how the equipment shown in Figure 7 could be used to find the mass of oxygen that combines with 0.500 g of iron wool in a crucible and lid of known mass.

(3)

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4 marks

2.24 g of iron combines with 0.96 g of oxygen to form an oxide of iron.

Determine the formula of this oxide of iron and use it to complete the balanced equation.

(relative atomic masses: Fe = 56.0, O = 16.0)

You must show your working.

balanced equation for the reaction is

................ Fe + ................O2 → ................................................

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71 mark

An atom has no overall charge because there are the same number of:

  • Protons and neutrons

  • Protons and electrons

  • Neutrons and electrons

  • Protons, neutrons and electrons

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8a1 mark

This question is about some of the elements in groups 1 and 2 of the periodic table.

The atomic number of lithium is 3. The mass number of a lithium atom is 7. Which row of the table shows the number of protons, neutrons and electrons in an atom of lithium-7?

 

 

Number of protons

Number of neutrons

Number of electrons

A

3

3

4

B

3

4

3

C

4

3

7

D

7

4

3

    8b1 mark

    Lithium, sodium and potassium are in group 1 of the periodic table.

    State, in terms of the electrons in their atoms, what the atoms of lithium, sodium and potassium have in common.

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    2 marks

    Magnesium has atomic number 12.

    Magnesium exists as magnesium-24, magnesium-25 and magnesium-26 atoms.

    Explain, in terms of protons and neutrons, why these atoms are isotopes of magnesium.

    8d2 marks

    Magnesium and calcium are in group 2 of the periodic table. They are less reactive than the metals in group 1.

    Calcium reacts with water to form calcium hydroxide, Ca(OH)2, and hydrogen, H2.

    Ca (s) + 2H2O (l) → Ca(OH)2 (s) + H2 (g)

    Describe what would be seen when a piece of calcium is dropped into a container of water.

    8e2 marks

    Magnesium reacts very slowly with cold water but it reacts faster with steam, H2O, to form magnesium oxide, MgO, and hydrogen.

    Write the balanced equation for the reaction between magnesium and steam.

    8f2 marks

    The electronic configurations of magnesium and calcium are

    magnesium 2.8.2
    calcium 2.8.8.2

    When magnesium and calcium react with water they form positive ions.

    Suggest an explanation, in terms of their electronic configurations, why calcium is more reactive than magnesium.

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    3 marks

    A sample of calcium bromide contains 0.2 g calcium and 0.8 g bromine by mass.

    Calculate the empirical formula of calcium bromide. (relative atomic masses: Ca = 40, Br = 80)

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    91 mark

    Which statement best describes the structure of an atom? 

    • A nucleus containing protons and neutrons, surrounded by electrons

    • A nucleus containing protons and electrons, surrounded by neutrons

    • A nucleus containing electrons and neutrons, surrounded by protons 

    • A nucleus containing protons, surrounded by neutrons and electrons

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    10a2 marks

    An atom of potassium has atomic number 19 and mass number 39.

    i) Give the electronic configuration of this potassium atom. (1)

    ii) This potassium atom forms the ion K+. Which row shows the number of protons and the number of neutrons in this potassium ion, K+? (1)    

     

    number of protons

    number of neutrons

    A

    19

    19

    B

    19 

    20

    C

    20 

    19

    D

    20

    20

    10b2 marks

    Potassium and caesium are in the same group of the periodic table.

    Explain, in terms of electrons, why potassium and caesium are in the same group.

    10c2 marks

    Fluorine boils at –188 °C. There are forces between fluorine molecules.

    Explain, in terms of these forces, why the boiling point of fluorine is low.

    10d3 marks

    Potassium reacts with fluorine to form potassium fluoride. Potassium fluoride is a solid.

    Complete the balanced equation for this reaction and add the state symbols.

    .................K (...........) + F2 (g) → .................KF (...........)

    10e1 mark

    What are the elements in group 1 of the periodic table called?

    • alkali metals

    • fullerenes 

    • halogens 

    • noble gases

    10f2 marks

    Figure 14 shows the melting points and boiling points of elements in group 7 of the periodic table.

    fig-14-q8f-1cho-2f-paper-1-nov-2020

    Figure 14

    i) Give, using Figure 14, the boiling point of bromine.

    (1)

    boiling point of bromine = ..................................... °C

    ii) State which two elements from Figure 14 are solids at room temperature.

    (1)

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    111 mark

    Higher Only 

    Element Cu has two isotopes. Their mass numbers are 63 and 65. 

    • Cu- 63 has a percentage abundance of 69.2%

    • Cu- 65 has a percentage abundance of 30.8% 

    Estimate the relative atomic mass of element Cu. 

    • Below 63

    • Between 63.5 and 64

    • Between 64 and 64.5

    • Above 64.5

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    1a3 marks

    Rutherford’s gold foil experiment led to the development of a different model of the atom.

    Describe Rutherford’s model of the atom.

    1b2 marks

    Atoms contain protons, neutrons and electrons. Their masses and charges are compared to each other and are known as relative atomic masses and relative atomic charges.

    Complete the table to show the correct relative atomic masses and charges.  

     

    Relative atomic mass

    Relative atomic charge

    proton

    1

    ……………..

    neutron

    ……………..

    0

    electron

    ……………..

    ……………..

    1c4 marks

    Explain why atoms have a neutral charge. 

    1d3 marks

    In terms of subatomic particles, compare the isotopes of carbon shown in the diagram below.

    straight C subscript 6 superscript 12          straight C subscript 6 superscript 13          straight C subscript 6 superscript 14

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    2a2 marks

    The atomic model developed by scientists has changed over time as experimental evidence improved understanding.

    Explain how Niels Bohr contributed to the atomic model. 

    2b3 marks

    Compare the relative atomic masses and relative atomic charges of the subatomic particles within an atom. 

    2c2 marks

    Higher Tier Only

    Figure 1 shows the percentage abundance of two isotopes of chlorine.

     

    Percentage abundance (%)

    Chlorine-35

    75

    chlorine-37

    25

    Figure 1

    Calculate the relative atomic mass of chlorine. 

    2d3 marks

    Explain why carbon-12 and carbon-13 are isotopes of the same element.

    Give your answer in terms of subatomic particles. 

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    3a5 marks

    Compare J.J. Thomson’s plum pudding model with Rutherford’s nuclear model of the atom. 

    3b2 marks

    Explain what isotopes are. 

    3c4 marks

    Explain how the gold foil experiment led to a better understanding of the nucleus. 

    3d5 marks

    Explain how the characteristics of subatomic particles within an atom contribute to the overall charge and mass of an atom. 

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    4a3 marks

    Explain the impact of the discoveries of the electrons, nucleus and neutron on the evolution of the atomic model. 

    4b3 marks

    Higher Tier Only

    Explain how the relative atomic mass of an element is calculated and use the example in figure 1 to illustrate your explanation. 

     

    Percentage abundance (%)

    Magnesium-24

    78.7

    Magnesium-25

    10.1

    Magnesium-26

    11.2

    Figure 1

    4c4 marks

    Explain the relationship between mass number and atomic number in determining the identity and properties of an element. Use carbon-12 and carbon-13 as an example. 

    4d3 marks

    Explain the structure of an atom according to the current atomic model. 

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    5a2 marks

    Bohr further developed the atomic model proposed by Rutherford.

    Compare the main features of Bohr’s improvement to the atomic model.

    5b3 marks

    Rutherford’s model of the atom improved the understanding of the atom. Explain how older models were limited in their understanding of the atom. 

    5c3 marks

    Explain why isotopes of an element will have similar chemical properties.

    5d2 marks

    Explain why an atom does not collapse inwards. 

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    6a3 marks

    Explain how Chadwick’s work on the atomic model led to a better understanding of the existence of isotopes. 

    6b3 marks

    The diagram below shows two atoms.

    edx-1-1-hard-paper-2-q1b

    Compare the structures of both atoms. 

    6c2 marks

    Explain why the atoms in part b) react in the same way. 

    6d2 marks

    Compare the mass number and atomic number of the atoms mentioned in question 1b. 

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    7a4 marks

    The Bohr model of the atom introduced significant advancements in atomic theory.

    Discuss the limitations of the earlier atomic models in explaining the behaviour of electrons within an atom. 

    7b4 marks

    The diagram below shows the chemical symbols of two isotopes of uranium.

    begin mathsize 36px style U subscript 92 superscript 235 end style                     begin mathsize 36px style U subscript 92 superscript 238 end style

    Explain why uranium-235 and uranium-238 are categorised as isotopes of the same element. 

    7c4 marks

    Explain the difference in charge between a magnesium atom and magnesium ion. 

    7d2 marks

    Higher Tier Only:

    The table in figure 1 shows three isotopes of magnesium with varying abundances.

    Explain why the relative atomic mass of magnesium is 24.3 and not a number closer to 24 or 26.

     

    Percentage abundance (%)

    Magnesium-24

    78.7

    Magnesium-25

    10.1

    Magnesium-26

    11.2

    Figure 1

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    8a3 marks

    Describe the limitations of Dalton’s atomic model and Thomson’s plum pudding model in describing the structure of the atom.

    8b3 marks

    Explain why the nucleus is described as a concentrated mass at the centre of an atom.

    8c2 marks

    Explain the structure of an atom according to the plum pudding model. 

    8d3 marks

    Explain what the discovery by J.J. Thomson was and what it proved. 

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    9a6 marks

    Explain the difference in charge of the nucleus of an atom and an atom as a whole. 

    9b3 marks

    Explain the structure of an atom according to the nuclear model. 

    9c3 marks

    Explain the contributions of different scientists to the understanding of the atomic structure.

    9d3 marks

    Explain the presence of forces within an atom and its impact. 

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    10a3 marks

    Higher Tier Only

    Explain why the masses and charges of subatomic particles are described as ‘relative atomic masses’ and ‘relative atomic charges’.

    10b4 marks

    Compare the relative sizes of the following things: atom, nucleus and electrons. 

    10c3 marks

    The diagram shows the chemical symbol of magnesium and lithium.

    Mg subscript 12 superscript 24                             begin mathsize 36px style Li subscript 3 superscript 7 end style

    Explain the difference in nucleon number of an atom of magnesium and the nucleon number of an atom of lithium. 

    10d2 marks

    Higher Tier Only

    Explain why percentage abundance of isotopes is taken into consideration when calculating the relative atomic mass. 

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