⚛️ NUCLEAR MODEL OF THE ATOM ⚛️

Cambridge IGCSE Physics - Complete Theory & Formulas

📌 SECTION 19.1: THE ATOM

🔬 What is an Atom?

An atom is the smallest unit of a chemical element that retains the properties of that element. Atoms are incredibly small - approximately 100 million atoms can fit across the width of your fingernail!

💡 Key Concept: Although atoms are the smallest units of elements, they are composed of even smaller subatomic particles: protons, neutrons, and electrons.

🎯 Structure of an Atom

Figure: Simplified model showing nucleus at center with electrons in orbits

An atom consists of two main components:

Nucleus - The central core containing positive charge and almost all the atom's mass
Electrons - Negatively charged particles orbiting around the nucleus

⚡ Important Facts:

The nucleus is extremely small compared to the atom's total size
Most of an atom is empty space
Opposite charges attract: positive nucleus attracts negative electrons
Electrons are held in orbit by electrostatic attraction

⚡ Formation of Ions

Positive Ions (Cations)

When an atom loses electrons, it has more positive charges than negative charges, forming a positive ion.

Figure: Formation of a positive ion by losing an electron

Negative Ions (Anions)

When an atom gains electrons, it has more negative charges than positive charges, forming a negative ion.

📝 Ion Formation Rules:
Neutral Atom - electrons → Positive Ion
Neutral Atom + electrons → Negative Ion

🎯 Rutherford's Gold Foil Experiment (1911)

Scientists Geiger and Marsden, under the supervision of Ernest Rutherford, performed a groundbreaking experiment that revealed the nuclear structure of atoms.

Figure: Alpha particle scattering experiment setup

📊 Experimental Observations:

Most α-particles passed straight through the gold foil without deflection
A few α-particles were deflected at large angles
Very few α-particles bounced back (approximately 1 in 8000)

🧠 Rutherford's Conclusions:

Evidence for the Nuclear Model:

🌌 Atoms are mostly empty space - explains why most α-particles pass through
⚫ Very small nucleus - only a tiny fraction of the atom's volume
⚖️ Massive nucleus - contains almost all the atom's mass
➕ Positively charged nucleus - repels positive α-particles that come close

📌 SECTION 19.2: THE NUCLEUS

🔬 Composition of the Nucleus

The nucleus consists of two types of particles called nucleons:

Protons - Positively charged particles
Neutrons - Neutral particles (no charge)

Figure: Structure of helium nucleus showing protons and neutrons

⚡ Relative Charges of Atomic Particles

Particle	Symbol	Relative Charge	Approximate Mass (amu)	Location
Proton	p or ¹₁H	+1	1	Nucleus
Neutron	n or ¹₀n	0	1	Nucleus
Electron	e⁻ or ⁰₋₁e	-1	1/2000 (negligible)	Orbits/Shells

📊 Proton Number (Atomic Number) - Z

Proton Number (Z) = Number of protons in the nucleus

💡 Key Points:

Z is unique for each element
Defines the identity of the element
In a neutral atom: Number of electrons = Z
Example: All carbon atoms have Z = 6

📊 Nucleon Number (Mass Number) - A

Nucleon Number (A) = Total number of protons + neutrons

Number of Neutrons = A - Z

🔤 Nuclide Notation

📝 Example: Carbon-12

¹²₆C

Element: Carbon (C)
Proton number (Z) = 6 → 6 protons
Nucleon number (A) = 12 → 12 total nucleons
Neutrons = A - Z = 12 - 6 = 6 neutrons
Electrons (neutral atom) = 6

🔬 Isotopes

Definition: Isotopes are atoms of the same element that have:

✅ The same number of protons (same Z)
❌ Different numbers of neutrons (different A)

Example: Three Isotopes of Carbon

Isotope	Notation	Protons (Z)	Neutrons (A-Z)	Electrons	Mass
Carbon-12	¹²₆C	6	6	6	12 amu
Carbon-13	¹³₆C	6	7	6	13 amu
Carbon-14	¹⁴₆C	6	8	6	14 amu

⚠️ Important: Isotopes of the same element have identical chemical properties because they have the same number of electrons and electron configuration.

📌 SECTION 19.3: NUCLEAR FISSION AND NUCLEAR FUSION

💥 Nuclear Fission

Definition: Nuclear fission is a process in which a large, heavy nucleus splits into two smaller nuclei, releasing a huge amount of energy.

Figure: Nuclear fission of Uranium-235

📝 Example Fission Equation:

¹₀n + ²³⁵₉₂U → ¹⁴⁴₅₆Ba + ⁹⁰₃₆Kr + 2¹₀n + energy

✅ Conservation Laws in Nuclear Reactions:

1. Conservation of Nucleon Number:

Total A (before) = Total A (after)

Before: 1 + 235 = 236

After: 144 + 90 + 2(1) = 236 ✓

2. Conservation of Charge:

Total Z (before) = Total Z (after)

Before: 0 + 92 = +92

After: 56 + 36 + 2(0) = +92 ✓

🔢 Worked Example:

Problem: Find the missing values A and Z in this fission reaction:

²³³₉₂U + ¹₀n → ¹³⁷₅₄Xe + ^A_ZSr + 3¹₀n

Solution:

Step 1 - Find A (Nucleon Number):

Before: 233 + 1 = 234

After: 137 + A + 3(1) = 140 + A

Therefore: 140 + A = 234

A = 94

Step 2 - Find Z (Proton Number):

Before: 92 + 0 = +92

After: 54 + Z + 3(0) = 54 + Z

Therefore: 54 + Z = 92

Z = 38

Answer: ⁹⁴₃₈Sr (Strontium-94)

🌟 Nuclear Fusion

Definition: Nuclear fusion is a process in which two light atomic nuclei combine to form one heavier nucleus, releasing a huge amount of energy.

Figure: Nuclear fusion of hydrogen isotopes

📝 Example Fusion Equation:

²₁H + ³₁H → ⁴₂He + ¹₀n + energy

✅ Verification:

Nucleon conservation:

Before: 2 + 3 = 5

After: 4 + 1 = 5 ✓

Charge conservation:

Before: 1 + 1 = +2

After: 2 + 0 = +2 ✓

⚡ Mass-Energy Equivalence

Einstein's Mass-Energy Equation:

E = mc²

Where:

E = Energy released (Joules)
m = Mass converted (kilograms)
c = Speed of light = 3 × 10⁸ m/s

🔑 Key Concept: In both fission and fusion, the total mass after the reaction is slightly less than the mass before. This "missing mass" has been converted to energy according to Einstein's equation E = mc². Because c² is an enormous number, even a tiny amount of mass produces a huge amount of energy!

⚖️ Comparing Fission and Fusion

Property	Nuclear Fission	Nuclear Fusion
Process	Splitting large nucleus	Combining small nuclei
Starting Material	Heavy atoms (U-235, Pu-239)	Light atoms (H-2, H-3)
Products	2 medium nuclei + neutrons	1 heavier nucleus + neutrons
Conditions	Room temperature possible	Extremely high temperature & pressure
Energy Released	Very large	Even larger (per unit mass)
Difficulty	Easier to achieve	Very difficult to control
Current Use	Nuclear power plants	Sun & stars (not practical yet on Earth)
Chain Reaction	Self-sustaining (releases neutrons)	Not self-sustaining

🌍 Applications of Nuclear Energy

⚡ Nuclear Power Plants (Fission)

Generate approximately 10% of world's electricity
Use controlled fission of U-235 or Pu-239
Heat produced converts water to steam
Steam drives turbines to generate electricity
No greenhouse gas emissions during operation
Radioactive waste requires safe disposal

☀️ The Sun and Stars (Fusion)

Primary energy source for the Sun
4 million tons of mass converted to energy per second in the Sun
Temperature at Sun's core: ~15 million °C
Provides all energy for life on Earth
Scientists working on fusion reactors (ITER project)

📋 KEY FORMULAS SUMMARY

1. Number of Neutrons:
Number of neutrons = A - Z
(Nucleon number - Proton number)

2. Neutral Atom:
Number of electrons = Number of protons = Z

3. Relative Charge on Nucleus:
Nuclear charge = +Z
(Equal to proton number)

4. Relative Mass of Nucleus:
Nuclear mass ≈ A atomic mass units
(Approximately equal to nucleon number)

5. Mass-Energy Conversion:
E = mc²
Energy (J) = mass (kg) × [speed of light (m/s)]²

6. Conservation in Nuclear Reactions:
∑A (before) = ∑A (after)
∑Z (before) = ∑Z (after)

📊 IMPORTANT CONSTANTS & VALUES

Constant	Symbol	Value
Elementary charge	e	1.6 × 10⁻¹⁹ C
Speed of light	c	3.0 × 10⁸ m/s
Atomic mass unit	amu or u	1.66 × 10⁻²⁷ kg
Proton mass	m_p	1.673 × 10⁻²⁷ kg ≈ 1 amu
Neutron mass	m_n	1.675 × 10⁻²⁷ kg ≈ 1 amu
Electron mass	m_e	9.109 × 10⁻³¹ kg ≈ 1/2000 amu

🎯 QUICK REFERENCE GUIDE

🔹 To find number of protons: Look at Z (bottom number in nuclide notation)

🔹 To find number of neutrons: Calculate A - Z

🔹 To find number of electrons in neutral atom: Same as number of protons (Z)

🔹 To identify isotopes: Same Z, different A

🔹 To balance nuclear equations: Make sure ∑A and ∑Z are equal on both sides

⚠️ Common Mistakes to Avoid:

❌ Confusing mass number (A) with atomic number (Z)
❌ Forgetting that isotopes have same chemical properties
❌ Not balancing both nucleon number AND charge in nuclear equations
❌ Thinking electrons are in the nucleus (they orbit outside)
❌ Confusing ion formation with isotope differences

📝 PRACTICE PROBLEMS

Problem 1: An atom is represented as ²³₁₁Na. Determine:

a) Number of protons
b) Number of electrons (neutral atom)
c) Number of neutrons
d) Relative charge on nucleus

Answer:

a) Z = 11, so 11 protons
b) Neutral atom: 11 electrons
c) Neutrons = 23 - 11 = 12 neutrons
d) Nuclear charge = +11

Problem 2: Complete the nuclear fission equation:

²³⁵₉₂U + ¹₀n → ¹³⁹₅₆Ba + ^A_ZKr + 3¹₀n

Solution:

Nucleon balance: 235 + 1 = 139 + A + 3

236 = 142 + A → A = 94

Charge balance: 92 + 0 = 56 + Z + 0

92 = 56 + Z → Z = 36

Answer: ⁹⁴₃₆Kr (Krypton-94)

Problem 3: Identify which pairs are isotopes:

A) ¹²₆C and ¹⁴₆C
B) ¹⁶₈O and ¹⁶₇N
C) ³⁵₁₇Cl and ³⁷₁₇Cl

Answer:

A) ✅ Isotopes (same Z=6, different A)
B) ❌ Not isotopes (different Z)
C) ✅ Isotopes (same Z=17, different A)

📚 HISTORICAL MILESTONES

Year	Scientist	Discovery
1897	J.J. Thomson	Discovery of the electron
1911	Ernest Rutherford	Nuclear model of atom (gold foil experiment)
1913	Niels Bohr	Bohr's model with electron shells
1919	Ernest Rutherford	Discovery of the proton
1932	James Chadwick	Discovery of the neutron
1938	Otto Hahn & Fritz Strassmann	Discovery of nuclear fission
1942	Enrico Fermi	First controlled nuclear chain reaction

🎓 CONCLUSION

The nuclear model of the atom revolutionized our understanding of matter and energy. From Rutherford's groundbreaking gold foil experiment to modern nuclear physics, we've learned that:

⚛️ Atoms consist of a tiny, dense, positively charged nucleus surrounded by electrons
🔬 The nucleus contains protons and neutrons (nucleons)
🔢 Elements are defined by their proton number (Z)
⚖️ Isotopes are variants of elements with different neutron numbers
💥 Nuclear reactions can release enormous amounts of energy through fission or fusion
⚡ Mass and energy are interconvertible according to E = mc²

🌟 Remember: Understanding atomic structure is fundamental to chemistry, physics, and modern technology. From nuclear power to medical applications, the principles you've learned here have profound real-world implications!

End of Nuclear Model of the Atom

Cambridge IGCSE Physics - Complete Theory & Formulas Guide

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