The nucleus

1. Overview

The nucleus is the tiny, dense central core of an atom that contains nearly all of its mass. This topic explores how we describe the subatomic particles within the nucleus and how changes to this core result in the release of nuclear energy through fission and fusion.

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Key Definitions

• Nucleon: A particle found in the nucleus (either a proton or a neutron).
• Proton Number ($Z$): Also known as the atomic number; the number of protons in the nucleus of an atom.
• Nucleon Number ($A$): Also known as the mass number; the total number of protons and neutrons in the nucleus.
• Isotope: Atoms of the same element that have the same number of protons but a different number of neutrons.
• Nuclide: A distinct kind of atom or nucleus characterized by a specific number of protons and neutrons.

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Core Content

Composition of the Nucleus

The nucleus is made up of two types of particles, collectively called nucleons:

1. Protons: Positively charged particles.
2. Neutrons: Neutral particles (no charge).

Electrons are not in the nucleus; they orbit the nucleus in shells.

Relative Charges

In physics, we use "relative" charges to compare subatomic particles:

• Proton: +1
• Neutron: 0
• Electron: -1

Nuclide Notation

We use a standard symbol to describe a specific nucleus:

• $Z$ (Proton Number): Tells you the identity of the element.
• $A$ (Nucleon Number): Tells you the total mass.

Calculating the Number of Neutrons

To find the number of neutrons ($N$), subtract the proton number from the nucleon number: $N = A - Z$

Worked Example: A nucleus of Sodium is written as $^{23}_{11}\text{Na}$.

• Proton Number ($Z$) = 11
• Nucleon Number ($A$) = 23
• Number of Neutrons = $23 - 11 = 12$

Isotopes

An element can have different versions called isotopes.

• They have the same number of protons (so they are the same element).
• They have different numbers of neutrons (so they have different masses).
• Example: Carbon-12 ($^12_6\text{C}$) and Carbon-14 ($^14_6\text{C}$). Both have 6 protons, but Carbon-14 has two extra neutrons.

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Extended Content (Extended Curriculum Only)

Nuclear Mass and Charge

• Nuclear Charge: The relative charge of a nucleus is equal to its Proton Number ($Z$). For example, a Helium nucleus ($Z=2$) has a relative charge of +2.
• Nuclear Mass: Because protons and neutrons have almost identical masses and electrons have negligible mass, the relative mass of a nucleus is equal to its Nucleon Number ($A$).

Nuclear Fission

Fission is the splitting of a large, unstable nucleus (like Uranium-235) into two smaller "daughter" nuclei.

• Process: Usually triggered by the nucleus absorbing a neutron.
• Energy Change: The total mass of the particles after the split is slightly less than the mass before. This "lost" mass is converted into a huge amount of energy.

Nuclear Fusion

Fusion is the joining (fusing) of two small, light nuclei to form a single, larger nucleus.

• Process: Occurs in stars (like the Sun) where high temperatures and pressures force nuclei together.
• Energy Change: Similar to fission, the mass of the final large nucleus is slightly less than the combined mass of the original smaller nuclei. This mass difference is released as energy.

Balancing Nuclear Equations

In any nuclear equation, the total nucleon number (A) and the total proton number (Z) must be the same on both sides.

Worked Example: Alpha Decay Radium-226 undergoes alpha decay. Complete the equation. $$^{226}{88}\text{Ra} \rightarrow ^{?}{?}\text{X} + ^{4}_{2}\text{He}$$

1. Balance nucleon numbers: $226 = ? + 4$, so $? = 222$
2. Balance proton numbers: $88 = ? + 2$, so $? = 86$ (which is Radon, Rn)
3. Answer: $^{226}{88}\text{Ra} \rightarrow ^{222}{86}\text{Rn} + ^{4}_{2}\text{He}$

Worked Example: Beta Decay Carbon-14 undergoes beta decay. An electron ($^{0}{-1}\text{e}$) is emitted. $$^{14}{6}\text{C} \rightarrow ^{14}{7}\text{N} + ^{0}{-1}\text{e}$$ In beta decay: one neutron becomes a proton, so $Z$ increases by 1 but $A$ stays the same.

The most common exam mistake is reversing the proton and nucleon numbers (writing $^{88}{226}$ instead of $^{226}{88}$). Remember: $A$ (the bigger number) goes on top.

Fission/Fusion Equation (Qualitative)

$Nucleus_1 + Nucleus_2 \rightarrow Nucleus_{new} + Energy$

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Key Equations

Equation	Symbols	Units
$A = Z + N$	$A$: Nucleon number, $Z$: Proton number, $N$: Neutrons	None (Counting numbers)
Relative Nuclear Charge = $+Z$	$Z$: Proton number	None (Relative)
Relative Nuclear Mass $\approx A$	$A$: Nucleon number	None (Relative)

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Common Mistakes to Avoid

• ❌ Wrong: Adding the Proton Number and Nucleon Number together to find neutrons.
• ✅ Right: Always subtract the bottom number from the top number ($A - Z$) to find neutrons.
• ❌ Wrong: Thinking the top number ($A$) represents neutrons only.
• ✅ Right: The top number is the total of protons + neutrons.
• ❌ Wrong: Assuming electrons contribute to the mass of the atom.
• ✅ Right: Electrons have negligible mass; the mass is concentrated in the nucleus (protons and neutrons).
• ❌ Wrong: Swapping the positions of $A$ and $Z$ in notation.
• ✅ Right: Remember A is the Attic (top) and Z is the Zound (ground/bottom).

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Exam Tips

1. Check your subtraction: Many marks are lost on simple arithmetic when calculating neutron numbers. Double-check your $A - Z$ calculation.
2. Isotope Definition: If asked to define an isotope, always mention both that they have the same number of protons AND a different number of neutrons.
3. Fission vs. Fusion: To remember which is which, think of "Fission" as a "fissure" (a crack/split) and "Fusion" as "fusing" things together (like welding).

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0625 Theory papers.

Exam-Style Question 1 — Short Answer [5 marks]

Question:

The nuclide notation for an atom of uranium is $^{235}_{92}U$.

(a) State the number of protons in the nucleus of this atom. [1]

(b) State the number of neutrons in the nucleus of this atom. [1]

(c) Define the term isotope. [2]

(d) Uranium also exists as $^{238}{92}U$. Compare the number of protons and neutrons in an atom of $^{235}{92}U$ and an atom of $^{238}_{92}U$. [1]

Worked Solution:

(a)

1. The number of protons is the atomic number. $\boxed{92}$ [The atomic number is the subscript]

How to earn full marks:

• State the correct number (92).

(b)

1. The number of neutrons is the nucleon number minus the proton number. $235 - 92 = 143$ $\boxed{143}$ [Subtract the proton number from the nucleon number]

How to earn full marks:

• State the correct number (143).

(c)

1. Isotopes are atoms of the same element. [Same element means same number of protons]
2. But with different numbers of neutrons. [Different numbers of neutrons means different nucleon number/mass number]

How to earn full marks:

• State that isotopes are atoms of the same element.
• State that they have different numbers of neutrons.

(d)

1. Both isotopes have the same number of protons. [They are the same element]
2. $^{238}{92}U$ has 3 more neutrons than $^{235}{92}U$. [238 - 92 = 146 neutrons; 146 - 143 = 3]

How to earn full marks:

• State that both have the same number of protons.
• State that $^{238}_{92}U$ has more neutrons, or specifically 3 more.

Common Pitfall: Many students confuse the nucleon number and the proton number. Remember that the nucleon number is the total number of protons and neutrons, while the proton number is just the number of protons. Also, remember that isotopes of an element always have the same number of protons.

Exam-Style Question 2 — Short Answer [6 marks]

Question:

A radioactive source emits alpha particles. An experiment is set up to measure the number of alpha particles that pass through a thin sheet of aluminium.

(a) State what is meant by the term radioactivity. [1]

(b) The aluminium sheet is placed between the radioactive source and a detector. The count rate is recorded with and without the aluminium sheet in place. The results are shown below:

• Count rate without aluminium sheet: 520 counts/minute
• Count rate with aluminium sheet: 20 counts/minute

Explain what these results suggest about the penetrating power of alpha particles. [2]

(c) The half-life of the radioactive source is 10 days. Determine the time it takes for the count rate without the aluminium sheet to decrease to 65 counts/minute. [3]

Worked Solution:

(a)

1. Radioactivity is the spontaneous and random decay of unstable nuclei. [Two key aspects: spontaneous and random, plus a nucleus]

How to earn full marks:

• State that radioactivity involves the spontaneous decay of a nucleus.
• State that the decay is random.

(b)

1. The count rate decreases significantly when the aluminium sheet is placed in the path of the alpha particles. [Compare the two count rates]
2. This suggests that alpha particles have low penetrating power and are easily stopped by the aluminium sheet. [Relate the count rate decrease to penetrating power]

How to earn full marks:

• State that the count rate decreases significantly.
• Relate this decrease to the low penetrating power of alpha particles.

(c)

1. Determine the number of half-lives that have passed: $520 \div 2 = 260$, $260 \div 2 = 130$, $130 \div 2 = 65$ [Divide by 2 for each half-life]
2. Three half-lives have passed.
3. Calculate the total time: $3 \times 10 \text{ days} = 30 \text{ days}$ $\boxed{30 \text{ days}}$ [Multiply the number of half-lives by the half-life value]

How to earn full marks:

• Show the halving process (520 to 260 to 130 to 65).
• State that 3 half-lives have passed.
• Calculate the total time correctly with the correct unit.

Common Pitfall: When calculating half-life problems, make sure you understand what the question is asking. Sometimes you need to find the number of half-lives, and other times you need to find the time it takes for a certain number of half-lives to occur. Also, remember to include the correct units in your final answer.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

Nuclear fission is used in nuclear power plants to generate electricity.

(a) Describe the process of nuclear fission. Include in your description what happens to the nucleus and what is released during the process. [4]

(b) Write a nuclide equation to represent the fission of uranium-235 ($^{235}{92}U$) when bombarded with a neutron ($^{1}{0}n$), producing barium-141 ($^{141}{56}Ba$) and krypton-92 ($^{92}{36}Kr$). [2]

(c) Explain why nuclear fission is a chain reaction. [2]

Worked Solution:

(a)

1. Nuclear fission is the splitting of a heavy nucleus. [Start with the fundamental definition]
2. This happens when a neutron is absorbed by the nucleus. [Explain the trigger for fission]
3. The nucleus splits into two smaller nuclei (daughter nuclei). [Describe the products of fission]
4. Energy and more neutrons are released. [Key releases during fission, including neutrons for the chain reaction]

How to earn full marks:

• State that fission is the splitting of a heavy nucleus.
• State that a neutron is absorbed by the nucleus.
• State that the nucleus splits into two smaller nuclei.
• State that energy and more neutrons are released.

(b)

1. Write the equation showing the initial neutron and uranium. $^{235}{92}U + ^{1}{0}n \rightarrow$ [Reactants]
2. Write the equation showing the products (barium, krypton, and neutrons). $^{235}{92}U + ^{1}{0}n \rightarrow ^{141}{56}Ba + ^{92}{36}Kr + 3\ ^{1}_{0}n$ [Products] [Ensure the nucleon number and proton number are conserved on both sides of the equation. There must be 3 neutrons released in this case]

How to earn full marks:

• Write the correct reactants ($^{235}{92}U + ^{1}{0}n$).
• Write the correct products ($^{141}{56}Ba + ^{92}{36}Kr + 3\ ^{1}_{0}n$).

(c)

1. Nuclear fission releases neutrons. [Recall the neutron release from part (a)]
2. These neutrons can then be absorbed by other uranium nuclei, causing them to undergo fission. [Explain the propagation mechanism]
3. This process continues, creating a chain reaction. [Link the propagation to the chain reaction]

How to earn full marks:

• State that fission releases neutrons.
• State that these neutrons can be absorbed by other nuclei.
• State that this process continues, creating a chain reaction.

Common Pitfall: In describing nuclear fission, remember to include all the key components: the initial neutron absorption, the splitting of the heavy nucleus, the production of daughter nuclei, and the release of energy and more neutrons. Many students forget to mention the release of neutrons, which is crucial for understanding the chain reaction.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

Nuclear fusion is a process that occurs in stars.

(a) Define the term nuclear fusion. [2]

(b) Describe the conditions required for nuclear fusion to occur. [3]

(c) Explain why energy is released during nuclear fusion. [4]

Worked Solution:

(a)

1. Nuclear fusion is the joining of two light nuclei. [Key aspect: joining]
2. To form a heavier nucleus. [Key aspect: a heavier nucleus is the result]

How to earn full marks:

• State that fusion is the joining of light nuclei.
• State that a heavier nucleus is formed.

(b)

1. High temperature is required. [Mention the extreme temperature]
2. This is needed to overcome the electrostatic repulsion between the positively charged nuclei. [Explain why the temperature is needed]
3. High pressure/density is also required. [Mention the extreme pressure/density] [This is needed to increase the probability of collisions]

How to earn full marks:

• State that a high temperature is required.
• Explain that this is needed to overcome electrostatic repulsion.
• State that a high pressure/density is also required.

(c)

1. The mass of the new nucleus is less than the total mass of the original nuclei. [State the key mass difference]
2. This 'missing' mass is converted into energy. [Relate the mass difference to energy]
3. According to Einstein's equation, $E=mc^2$. [Mention mass-energy equivalence]
4. Where $E$ is energy, $m$ is mass, and $c$ is the speed of light. Since $c^2$ is a large number, even a small mass difference results in a large amount of energy being released. [Explain how the mass difference becomes a large amount of energy]

How to earn full marks:

• State that the mass of the new nucleus is less than the total mass of the original nuclei.
• State that this mass difference is converted into energy.
• Mention Einstein's equation, $E=mc^2$.
• Explain that a small mass difference results in a large amount of energy being released due to the large value of $c^2$.

Common Pitfall: When explaining why energy is released in nuclear fusion, it's important to clearly state that the mass of the product nucleus is less than the mass of the original nuclei. Many students get this backwards. Also, don't just state $E=mc^2$; explain how this equation relates to the mass difference and the large amount of energy released.