Leaving Certificate Physics

Modern Physics

Everything you need to know for the Leaving Cert — explained simply, with worked examples. No confusing jargon!

⚡ Chapter 21: The Electron ⚛️ Chapter 22: The Nucleus

⚡

The Electron

Charge, mass, energy units (eV)

Chapter 21

📺

Cathode Ray Tube

Thermionic emission, how a CRT works

Chapter 21

🩻

X-Rays

Production, properties, uses, hazards

Chapter 21

💡

Photoelectric Effect

Photons, Einstein's law, threshold frequency

Chapter 21

🔬

Atomic Structure

Rutherford's gold foil experiment

Chapter 22

🌈

Bohr Model & Spectra

Energy levels, emission line spectra

Chapter 22

☢️

Radioactivity

Alpha, beta, gamma — properties

Chapter 22

⏱

Half-Life

Half-life, decay constant, activity

Chapter 22

💥

Fission & Fusion

Nuclear reactions, E=mc², chain reactions

Chapter 22

📋

All Formulas

Quick reference sheet

Revision

💡 How to use this guide: Click any topic in the sidebar or above. Each section has simple explanations, key definitions to learn off, formulas with examples, and a quiz at the end. Work through them in order!

Chapter 21 — The Electron

⚡ The Electron & Energy

Learn about what makes up an atom, what an electron is, and how we measure really tiny amounts of energy.

🔵 Subatomic Particles

Every atom is made of three tiny particles. Think of it like this: the atom is like a tiny solar system — the nucleus is the sun in the middle, and electrons are like planets orbiting around it.

Particle	Mass	Charge	Where?
Proton	1 u	+1	In the nucleus
Neutron	1 u	0 (none)	In the nucleus
Electron	1/1840 u	−1	Orbits the nucleus

👉 u = unified atomic mass unit. 1 u = 1.66 × 10⁻²⁷ kg (incredibly small!)

In a neutral atom, the number of electrons equals the number of protons — so the charges cancel out.

⚡ The Electron in Detail

📖 Definition — Electron

An electron is an indivisible quantity of charge that orbits the nucleus of an atom.

Charge

−1.6 × 10⁻¹⁹ C

Negative charge (coulombs)

Mass

9.1 × 10⁻³¹ kg

Extremely light!

Charge (simpler)

−e

We often just call it "−1"

🧠 Why negative? Because electrons are attracted to positive things (like the nucleus) and repelled by negative things. This is why electrons stay orbiting the nucleus — opposite charges attract!

🔋 Energy of an Electron

When an electron is in an electric field (between two charged plates, like a battery), it can be speeded up — it gains kinetic energy. The amount of energy depends on the voltage (how strong the electric field is).

⚠️ Formula — Energy of a Charged Particle

E = qV

E = energy (joules, J)
q = charge on the particle (coulombs, C)
V = voltage (volts, V)

⚡ The Electronvolt (eV)

The amounts of energy involved with electrons are incredibly tiny. A joule is way too big a unit! So physicists invented a smaller unit: the electronvolt.

📖 Definition — Electronvolt

1 eV is the energy gained (or lost) by an electron when it moves through a potential difference (voltage) of 1 volt.

1 eV =

1.6 × 10⁻¹⁹ J

1 keV =

1 000 eV

1 MeV =

1 000 000 eV

1 GeV =

10⁹ eV

Converting eV → Joules

E(J) = E(eV) × 1.6 × 10⁻¹⁹

Multiply by 1.6 × 10⁻¹⁹ to convert from eV to joules

⚡ Energy Conversion Formula

When an electron is accelerated through a voltage, all its potential energy converts to kinetic energy. This gives us a very important formula:

⚠️ Formula — Energy Conversion in Electric Field

qV = ½mv²

q = charge on the particle (1.6 × 10⁻¹⁹ C for electron)
V = voltage (volts)
m = mass of electron (9.1 × 10⁻³¹ kg)
v = velocity/speed of the electron (m/s)

💡 Think of it like this: The electrical energy (qV) ALL turns into movement energy (½mv²). It's like converting a battery's energy into speed — none is wasted in this idealised case!

Chapter 21 — The Electron

🔥 Thermionic Emission & the Cathode Ray Tube

How do we get a beam of electrons? By heating metal! This is what old TVs used to work.

🌡️ Thermionic Emission

📖 Definition — Thermionic Emission

Thermionic emission is the emission of electrons from the surface of a hot metal.

Think of metal as a sea of free electrons swimming around between the atoms. Normally they don't have enough energy to escape. But when you heat the metal to over 800°C, the electrons gain so much energy they can break free from the surface — like water evaporating!

📖 Definition — Work Function (Φ)

The work function (Φ) of a metal is the minimum energy needed to remove the loosest electrons from the surface of that metal.

🧠 Easy way to remember: Work function = the "entrance fee" for escaping the metal. If the electron doesn't have enough energy to pay the fee, it stays inside!

📺 The Cathode Ray Tube (CRT)

A cathode ray tube uses thermionic emission to make a beam of electrons that can be controlled and directed at a screen. Old TVs and computer monitors used CRTs!

Structure of a Cathode Ray Tube

Parts of the CRT:

Part	What it does
Filament	Heated by a low voltage — it heats up the cathode
Cathode	Gets hot and emits electrons (thermionic emission)
Anode	Has a high positive voltage — attracts and accelerates electrons. Has a hole so electrons can pass through.
Y-plates	Deflect the beam UP or DOWN (vertical)
X-plates	Deflect the beam LEFT or RIGHT (horizontal)
Fluorescent screen	Glows where electrons hit it — producing a bright spot (scintillation)
Vacuum	No air inside — so electrons aren't stopped by gas molecules

🧲 Deflection of Electrons

Because electrons are negatively charged, they are deflected by both electric fields and magnetic fields:

Electric Field

→ Parabola

Attracted to +ve plate, repelled from −ve plate. Path curves like throwing a ball sideways.

Magnetic Field

→ Circle

Force is always perpendicular to motion. This makes the electrons travel in a circle!

🧮 Force in a Magnetic Field

⚠️ Formula — Force on Charged Particle in Magnetic Field

F = qvB

F = force (newtons, N)
q = charge (coulombs, C)
v = velocity/speed (m/s)
B = magnetic flux density (tesla, T)

When the electron moves in a circle in the magnetic field, the magnetic force = centripetal force:

Circular Motion in Magnetic Field (Higher Level)

qvB = mv²/r

r = radius of circular path (m)
Rearranging: r = mv/(qB)

📡 Applications of the CRT

CRO (Oscilloscope)

Displays electrical signals on a screen. Used in science labs.

ECG

Electrocardiogram — shows electrical signals from the heart

EEG

Electroencephalogram — shows electrical activity in the brain

Old TVs

Used three electron beams (red, blue, green) to produce colour images

🧪 Properties of Cathode Rays

Cathode rays (beams of electrons) have these important properties:

Travel in straight lines from the cathode
Have kinetic energy
Are deflected by electric and magnetic fields (proving negative charge)
Cause certain substances (like zinc sulphide) to fluoresce (glow)
Produce X-rays when hitting a metal target at high speed

Chapter 21 — The Electron

🩻 X-Rays

X-rays are like super-powered light that can pass through your body. Here's how they're made and used.

📖 Definition — X-Rays

X-rays are electromagnetic radiation of extremely high frequency (and short wavelength).

🔧 How X-Rays are Produced

X-rays are produced in the same way as a CRT but in reverse — instead of using electrons to make light on a screen, we smash electrons into a metal target to produce X-rays.

Step 1

Filament heats cathode → thermionic emission (electrons released)

Step 2

Very high voltage (>50 kV) accelerates electrons at high speed toward the anode

Step 3

Electrons smash into tungsten target in the anode

Step 4

Only 1% of energy makes X-rays. 99% produces heat (so there's oil cooling!)

💡 X-rays are the INVERSE of the photoelectric effect!
• X-ray production: Electrons IN → X-rays OUT
• Photoelectric effect: Light IN → Electrons OUT

🔩 The X-Ray Tube

Component	Purpose
Hot cathode	Produces electrons by thermionic emission
Vacuum	Nothing slows down the electrons
Tungsten target	Hard metal that produces X-rays when hit
High anode voltage (>50 kV)	Accelerates electrons to high speed
Lead shield	Protects the operator — only lets X-rays out through a small window
Oil coolant	Removes the 99% of energy that becomes heat

✨ Properties of X-Rays

Electromagnetic

They are EM waves — high frequency, short wavelength

Penetration

Pass through soft tissue (muscle) but NOT through dense material (bone, metal)

Ionisation

They knock electrons off atoms — creating ions. This can damage DNA!

Travel at c

Speed of light = 3 × 10⁸ m/s (they're light!)

🏥 Uses of X-Rays

Medicine: Detecting broken bones, cracks — bone absorbs X-rays (shows white on image)
Industry: Detecting cracks in metals, welds that can't be seen from outside
Security: Airport luggage scanners

☣️ Hazards of X-Rays

X-rays are dangerous because they ionise cells in living tissue. This means they can damage DNA, causing cells to mutate and potentially leading to cancer.

🎯 Exam question: "Why is lead shielding placed over the testes/ovaries when getting an X-ray?"
Answer: Lead shielding protects the reproductive organs from X-ray radiation, which could damage reproductive cells (which are particularly sensitive to ionising radiation). This prevents potential genetic damage.

Chapter 21 — The Electron

💡 The Photoelectric Effect

What happens when you shine light on a metal? Sometimes electrons fly out! Einstein figured out why — and it changed physics forever.

📖 Definition — Photoelectric Effect

The photoelectric effect is the emission of electrons from the surface of a metal due to electromagnetic radiation of a suitable frequency hitting the metal.

💡 What is a Photon?

📖 Definition — Photon

A photon is a bundle (or packet) of light energy.

Einstein realised that light isn't just a wave — it also comes in packets called photons. Each photon carries a specific amount of energy that depends on its frequency.

⚠️ Formula — Energy of a Photon

E = hf

E = energy of the photon (joules, J)
h = Planck's constant = 6.6 × 10⁻³⁴ J·s (given in exam)
f = frequency of the light (Hz)

🧠 Key idea: Higher frequency light = more energetic photons. This is why UV light (high frequency) can cause sunburn but visible light (lower frequency) doesn't — UV photons carry more energy!

💥 How the Photoelectric Effect Works

When a photon hits a metal surface, it gives ALL its energy to ONE electron. If the photon's energy is greater than the work function (Φ), the electron can escape. If not — nothing happens!

Photon energy < Φ

❌ No emission

Electron can't escape, even with lots of photons!

Photon energy ≥ Φ

✅ Emission!

Electron escapes. Extra energy becomes kinetic energy.

🔁 Effect of Frequency vs Intensity

Change this...	Effect on electrons emitted
Higher frequency	Each electron emitted has MORE kinetic energy (moves faster)
Higher intensity (brighter light)	MORE electrons are emitted per second (but same energy each)

🧠 Analogy: Imagine throwing balls at a wall to knock bricks out. The frequency = how hard each ball is thrown. The intensity = how many balls you throw per second. Harder throws = more energy per brick. More balls = more bricks knocked out.

📐 Threshold Frequency (f₀)

📖 Definition — Threshold Frequency

The threshold frequency (f₀) is the minimum frequency of electromagnetic radiation needed to cause photoelectric emission from a given metal.

Work Function Formula

Φ = hf₀

Φ = work function (J)
h = Planck's constant
f₀ = threshold frequency (Hz)

⚡ Einstein's Photoelectric Law (Higher Level)

📖 Einstein's Photoelectric Law

The energy of the fastest emitted electron equals the difference between the energy of the photon and the work function of the metal.

⚠️ Formula — Einstein's Photoelectric Equation (HL)

hf = Φ + ½mv²_max

hf = energy of incoming photon
Φ = work function of the metal (energy to escape)
½mv²_max = maximum kinetic energy of emitted electron

💡 Plain English version: Photon energy = Work to escape + Leftover speed energy. The photon pays the "entry fee" (work function) and gives the rest to the electron as speed!

📱 Photocell

A photocell is a device that uses the photoelectric effect to convert light into electric current. Light hits the cathode → electrons are released → they flow to the anode → current flows!

Applications: Burglar alarms, smoke detectors, automatic doors, light meters, solar panels, optical soundtracks in films.

Chapter 21 — Worked Examples

📐 Calculations: Chapter 21

Step-by-step worked examples from your textbook — I'll explain exactly what's happening at each stage.

🧮 Example 1 — Converting MeV to Joules

Q: What is the energy of 5.6 MeV in joules?

Step 1 — Convert MeV to eV

5.6 MeV = 5.6 × 10⁶ eV
(1 MeV = 1,000,000 eV = 10⁶ eV)

Step 2 — Use conversion formula: E(J) = E(eV) × 1.6 × 10⁻¹⁹

E(J) = (5.6 × 10⁶) × (1.6 × 10⁻¹⁹)
E(J) = 8.96 × 10⁻¹³ J

✅ Answer: 8.96 × 10⁻¹³ joules

🧮 Example 2 — Finding Velocity of Electron (from voltage)

Q: An electron (charge = 1.6 × 10⁻¹⁹ C, mass = 9.1 × 10⁻³¹ kg) has 1 eV of kinetic energy. Find its velocity.

Step 1 — Convert energy to joules

1 eV = 1.6 × 10⁻¹⁹ J

Step 2 — Use qV = ½mv². The KE = 1.6 × 10⁻¹⁹ J

1.6 × 10⁻¹⁹ = ½ × (9.1 × 10⁻³¹) × v²

Step 3 — Rearrange for v

v² = 2 × (1.6 × 10⁻¹⁹) / (9.1 × 10⁻³¹)
v² = 3.52 × 10¹¹
v = √(3.52 × 10¹¹) = 5.93 × 10⁵ m/s

✅ Answer: 5.93 × 10⁵ m/s (about 593,000 m/s!)

🧮 Example 3 — Force & Radius in Magnetic Field (HL)

Q: An electron (v = 4 × 10⁷ m/s) enters a magnetic field (B = 5 × 10⁻² T) at right angles. Find: (i) the force, (ii) the radius of its circular path. (q = 1.6 × 10⁻¹⁹ C, m = 9.1 × 10⁻³¹ kg)

Part (i) — Force: F = qvB

F = (1.6 × 10⁻¹⁹)(4 × 10⁷)(5 × 10⁻²)
F = 3.2 × 10⁻¹³ N

Part (ii) — Radius: Set F = mv²/r, so r = mv²/F

r = (9.1 × 10⁻³¹)(4 × 10⁷)² / (3.2 × 10⁻¹³)
r = (9.1 × 10⁻³¹)(16 × 10¹⁴) / (3.2 × 10⁻¹³)
r = 4.55 × 10⁻³ m

✅ Force = 3.2 × 10⁻¹³ N, Radius = 4.55 × 10⁻³ m (about 4.5 mm)

🧮 Example 4 — Energy of a Photon

Q: Calculate the energy of a photon of violet light with wavelength 420 nm. (h = 6.6 × 10⁻³⁴ Js, c = 3.0 × 10⁸ m/s)

Step 1 — Find frequency using c = fλ

f = c / λ = (3 × 10⁸) / (420 × 10⁻⁹) = (3 × 10⁸) / (4.2 × 10⁻⁷)
f = 7.14 × 10¹⁴ Hz

Step 2 — Find energy using E = hf

E = (6.6 × 10⁻³⁴)(7.14 × 10¹⁴) = 4.71 × 10⁻¹⁹ J

✅ Answer: 4.71 × 10⁻¹⁹ J (or about 2.9 eV)

🧮 Example 5 — Threshold Frequency & Max Velocity (HL)

Q: Zinc has work function 4.3 eV. UV light of wavelength 240 nm shines on it. Find: (i) threshold frequency, (ii) max velocity of emitted electrons.

Part (i) — Convert work function to Joules

Φ = 4.3 × 1.6 × 10⁻¹⁹ = 6.88 × 10⁻¹⁹ J

Then use Φ = hf₀ to find threshold frequency

f₀ = Φ/h = (6.88 × 10⁻¹⁹) / (6.6 × 10⁻³⁴) = 1.04 × 10¹⁵ Hz

Part (ii) — Find frequency of 240 nm light

f = c/λ = (3 × 10⁸)/(2.4 × 10⁻⁷) = 1.25 × 10¹⁵ Hz

Apply Einstein's photoelectric equation: hf = Φ + ½mv²

(6.6×10⁻³⁴)(1.25×10¹⁵) = (6.88×10⁻¹⁹) + ½(9.1×10⁻³¹)v²
8.25×10⁻¹⁹ = 6.88×10⁻¹⁹ + ½(9.1×10⁻³¹)v²
1.37×10⁻¹⁹ = ½(9.1×10⁻³¹)v²
v² = (2 × 1.37×10⁻¹⁹)/(9.1×10⁻³¹) = 3.01×10¹¹
v = 5.48 × 10⁵ m/s

✅ f₀ = 1.04 × 10¹⁵ Hz, v_max = 5.48 × 10⁵ m/s

Chapter 21 — Quiz

✅ Quiz: Chapter 21

Test yourself! Click on the answer you think is correct.

Chapter 22 — The Nucleus

🔬 Atomic Structure & Rutherford's Experiment

How did scientists figure out what's inside an atom? Rutherford's gold foil experiment changed everything!

🍮 The Old Model — "Plum Pudding"

Before 1909, scientists thought the atom was like a plum pudding — a uniform blob of positive charge with electrons scattered through it like raisins. This was J.J. Thomson's model.

🥇 Rutherford's Gold Foil Experiment (1909)

Ernest Rutherford fired alpha particles (helium nuclei — fast, positive, heavy) at a very thin sheet of gold foil. He expected them to pass straight through (based on the plum pudding model).

What he expected

All particles pass straight through (plum pudding model)

What actually happened

Most went straight through BUT a few bounced back at large angles!

🧠 Rutherford said: "It was as incredible as if you fired a 15-inch shell at a piece of paper and it came back and hit you!"

Conclusions from the experiment:

Most of the atom is empty space (most particles passed straight through)
There is a very small, dense positive core called the nucleus
Electrons orbit the nucleus at a distance
Radius of nucleus ≈ 10⁻¹⁵ m; radius of atom ≈ 10⁻¹⁰ m (nucleus is 100,000× smaller!)

🎯 Exam question: "Why was the experiment carried out in a vacuum?"
Answer: To prevent the alpha particles from colliding with air molecules (which would scatter them), and because the range of alpha particles in air is very short.

🔢 The Nucleus

Atomic Number (Z)

Z

Number of protons in the nucleus (defines the element)

Mass Number (A)

A

Total number of protons + neutrons (nucleons)

Neutron Number

A − Z

Number of neutrons = mass number minus atomic number

Chemical Symbol Notation

ᴬ_Z X

X = chemical symbol (e.g., C for Carbon)
A = mass number (top number)
Z = atomic number (bottom number)
Example: ¹²₆C = Carbon with 6 protons and 6 neutrons

🧬 Isotopes

📖 Definition — Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons (different mass numbers).

Example: Carbon-12 (¹²₆C) and Carbon-14 (¹⁴₆C) are both carbon but with different neutron numbers. Carbon-14 is radioactive and used in carbon dating!

Chapter 22 — The Nucleus

🌈 Bohr Model & Emission Spectra

Niels Bohr figured out why atoms glow in specific colours. Each element has its own "colour fingerprint"!

🪐 The Bohr Model of the Atom

Niels Bohr (1913) proposed that electrons orbit the nucleus in fixed circular paths called energy levels (or shells). Each orbit is at a specific distance from the nucleus:

Smallest orbit = lowest energy level
Larger orbits = higher energy levels
Electrons can jump between levels if they absorb or emit the right amount of energy

🧠 Think of it like steps on a staircase — electrons can only be on a step, never between steps. To jump up, they need energy. When they jump down, they release energy as light!

🌈 Emission Line Spectra

When energy is given to a gas (e.g., by heating it or passing electricity through it), electrons jump to higher energy levels. When they fall back down, they emit a photon of light with a specific frequency.

⚠️ Formula — Emission Line Spectra

hf = E₂ − E₁

h = Planck's constant
f = frequency of emitted radiation
E₂ = higher energy level (electron starts here)
E₁ = lower energy level (electron ends here)
The difference in energy is emitted as a photon of light

Since each element has different energy levels, each element emits different specific frequencies — giving a unique "barcode" of colours called an emission line spectrum.

🌈 Practical Use of Line Spectra

Identifying elements in distant stars! By looking at the light from a star through a spectrometer, we can identify which elements are present — even though the star is billions of km away!

☀️ Continuous Spectra

When a solid metal is heated (like the filament in a light bulb), the electrons gain a continuous range of energies — so they emit ALL frequencies of light. This produces a rainbow (continuous spectrum), not individual lines.

Emission Line Spectrum

Specific lines of colour. From hot gases. Each element has unique lines.

Continuous Spectrum

Full rainbow. From hot solids/liquids. All frequencies present.

Chapter 22 — The Nucleus

☢️ Radioactivity

Some atoms are unstable and break apart, releasing energy and particles. This is radioactivity!

📖 Definition — Radioactivity

Radioactivity is the spontaneous emission of radiation due to the natural disintegration of an unstable nucleus.

📖 Definition — Radiation

Radiation is the emission of particles of matter or photons of energy from a nucleus.

🧠 Key word: SPONTANEOUS — it happens by itself, randomly, without any trigger. You can't make a radioactive atom decay faster by heating it, pressurising it, etc.

Three Types of Radiation

α

Alpha Radiation

What it is: Helium nucleus (2 protons + 2 neutrons)

Charge: +2
Mass: 4 u (heavy!)

Ionisation: Very high ⬆️
Penetration: Very low ⬇️
Stopped by: Paper or a few cm of air

β

Beta Radiation

What it is: Fast electron emitted from nucleus

Charge: −1
Mass: 1/1840 u (very light)

Ionisation: Medium
Penetration: Medium
Stopped by: A few mm of aluminium

γ

Gamma Radiation

What it is: High-energy EM radiation (photon)

Charge: 0 (none)
Mass: 0 (massless!)

Ionisation: Low
Penetration: Very high ⬆️
Stopped by: Several cm of lead

🧠 Memory trick for penetration: Alpha = A for "A tiny bit" (stopped by paper), Beta = Better than alpha (stopped by aluminium), Gamma = Goes through almost everything (stopped by lead). A-B-G = increasing penetration!

🧠 Ionisation vs Penetration are OPPOSITES: The more ionising a particle is, the LESS penetrating it is. Alpha is very ionising but barely penetrates. Gamma barely ionises but goes through everything!

Deflection in Electric & Magnetic Fields

Radiation	Deflection in E-field	Deflection in B-field
Alpha (α)	Deflected toward −ve plate (small deflection — heavy)	Deflected (circular path)
Beta (β)	Deflected toward +ve plate (larger deflection — light)	Deflected in opposite direction to alpha
Gamma (γ)	NOT deflected (no charge)	NOT deflected (no charge)

☢️ Background Radiation

📖 Definition — Background Radiation

Background radiation is radiation that comes from environmental sources including the Earth's crust, the atmosphere, cosmic rays, and radioisotopes.

We are all exposed to low levels of radiation all the time from natural sources (radon gas, granite rocks, cosmic rays from space). This is called background radiation and is generally harmless at normal levels.

🔬 Ionisation

📖 Definition — Ionisation

Ionisation is the charging of a neutral atom or molecule when it loses or gains one or more electrons.

All three types of radiation can ionise atoms — but α does it most, γ does it least. Ionising radiation is dangerous to living cells because it damages DNA.

Chapter 22 — The Nucleus

💥 Nuclear Decay Equations

When an atom decays, it turns into a different element! Learn how to write and balance nuclear equations.

📐 Rules for Nuclear Equations

In a nuclear equation, two things must be conserved (stay the same on both sides):

Mass Numbers (top)

The sum of all mass numbers (A) on the left = sum on the right

Atomic Numbers (bottom)

The sum of all atomic numbers (Z) on the left = sum on the right

🔴 Alpha Decay

📖 Definition — Alpha Emission

Alpha emission is the emission of a helium nucleus (²He or α) from a large, unstable atom.

Alpha Decay — What happens to the nucleus?

Mass number: −4 Atomic number: −2

The atom loses 2 protons and 2 neutrons → becomes a completely different element!
Example: Uranium-238 → Thorium-234 + Alpha
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

📝 How to check this equation

²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He

Check mass numbers (top): LEFT = 238, RIGHT = 234 + 4 = 238 ✅

They balance!

Check atomic numbers (bottom): LEFT = 92, RIGHT = 90 + 2 = 92 ✅

They balance!

✅ Valid equation — both sides conserve mass number and atomic number

🔵 Beta Decay

📖 Definition — Beta Emission

Beta emission is the emission of an electron (⁻¹e or β) when a neutron decays into a proton inside the nucleus.

Beta Decay — What happens to the nucleus?

Mass number: 0 Atomic number: +1

A neutron → proton + electron (emitted). Mass number unchanged, atomic number increases by 1!
Example: Carbon-14 → Nitrogen-14 + Beta
¹⁴₆C → ¹⁴₇N + ⁰₋₁e

🧠 Beta emission in plain English: A neutron inside the nucleus splits into a proton (stays in nucleus) and an electron (shoots out at high speed as beta particle). One more proton = different element!

🟣 Gamma Emission

Gamma radiation is just energy released from an excited nucleus — no particles are emitted. So:

Gamma Emission

Mass number: 0 Atomic number: 0

Gamma emission does NOT change the element. It just releases excess energy.
It usually happens AFTER alpha or beta decay when the new nucleus is left in an excited state.

Chapter 22 — The Nucleus

⏱ Half-Life & Radioactive Decay

Radioactive decay is random — but we can measure how quickly a sample decays using half-life.

📖 Definition — Half-Life (T½)

The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.

🧠 Think of it like halving a pizza: Every half-life, you eat half of what's left. After 1 half-life = ½ left. After 2 = ¼. After 3 = ⅛. And so on!

📉 How Half-Life Works

Number of Half-Lives	Fraction of Sample Remaining
0	1 (all of it)
1	½
2	¼ (= 1/2²)
3	⅛ (= 1/2³)
n	1/2ⁿ

📊 Activity

📖 Definition — Activity (A)

The activity of a radioactive source is the number of decays (disintegrations) per second. Measured in becquerels (Bq). 1 Bq = 1 decay per second.

📖 Definition — Decay Constant (λ)

The decay constant (λ) is the probability that an individual nucleus will decay in one second.

🔢 Key Formulas

⚠️ Law of Radioactive Decay (HL)

A = λN

A = activity (Bq = decays per second)
λ = decay constant (s⁻¹)
N = number of undecayed nuclei in the sample

⚠️ Half-Life & Decay Constant (HL)

T½ = ln2 / λ = 0.693 / λ

T½ = half-life (seconds)
λ = decay constant (s⁻¹)
ln2 = 0.693 (natural log of 2)

🌍 Uses of Radioactive Decay

Carbon Dating

Carbon-14 (half-life 5,730 years) used to date ancient organic materials

Medical Tracers

Short half-life isotopes injected to track blood flow or diagnose disease

Nuclear Power

Long half-life uranium used as fuel in nuclear reactors

Smoke Detectors

Americium-241 ionises air — smoke interrupts the current, triggering alarm

Chapter 22 — The Nucleus

💥 Fission & Fusion

Two ways to get ENORMOUS amounts of energy from atoms — splitting them or joining them!

🔀 E = mc² — Einstein's Equation

Einstein showed that mass and energy are two forms of the same thing. A tiny amount of mass can be converted into an enormous amount of energy!

⚠️ Mass-Energy Equivalence

E = mc²

E = energy (joules)
m = mass lost/converted (kg)
c = speed of light = 3 × 10⁸ m/s

Because c² = 9 × 10¹⁶, even a tiny mass produces ENORMOUS energy!

🧠 Why is nuclear energy so powerful? Because c² is such a huge number (90,000,000,000,000,000). So even losing 1 kg of mass would release 9 × 10¹⁶ joules — enough to power a city for years!

💥 Nuclear Fission

📖 Definition — Nuclear Fission

Nuclear fission is the splitting of a large nucleus into two smaller nuclei (of roughly equal mass), with the emission of neutrons and release of energy.

Example — Fission of Uranium-235

A slow neutron hits Uranium-235, which splits into Xenon-143 and Strontium-90 plus 3 neutrons and energy:

The equation

²³⁵₉₂U + ¹₀n → ¹⁴³₅₄Xe + ⁹⁰₃₈Sr + 3(¹₀n) + energy

Check mass numbers: 235+1 = 236 = 143+90+3(1) = 236 ✅

They balance!

⛓️ Chain Reactions

📖 Definition — Chain Reaction

A chain reaction is a reaction where at least one neutron is released during each fission reaction, which then causes further fissions — it is self-sustaining.

📖 Definition — Critical Mass

Critical mass is the minimum amount of fissile material needed for chain reactions to occur.

🌟 Nuclear Fusion

📖 Definition — Nuclear Fusion

Nuclear fusion is the combining of two small nuclei to form a single larger nucleus, with the release of energy.

Fusion is what powers the Sun! Hydrogen isotopes (deuterium and tritium) are fused together at extremely high temperatures to form helium, releasing enormous energy.

Fission vs Fusion

Fission: Split large atoms (uranium). Used in nuclear power plants. Produces radioactive waste.

Fusion: Join small atoms (hydrogen). Powers stars. Much cleaner but extremely hard to control on Earth.

🎯 Why is it hard to achieve fusion on Earth?
To fuse nuclei, you need extremely high temperatures (millions of degrees) to overcome the repulsion between the positively charged nuclei. This requires more energy to initiate than current technology can sustain.

Chapter 22 — The Nucleus

🏭 Nuclear Reactors

A nuclear reactor is basically a very controlled fission chain reaction used to generate electricity.

⚙️ Components of a Nuclear Reactor

Component	Function
Fuel rods	Usually uranium-235 — the source of fission energy
Moderator	Slows down fast neutrons so they can cause more fission (e.g., graphite or heavy water)
Control rods	Absorb neutrons to control the reaction speed (e.g., boron rods). Push in = slow down, pull out = speed up
Coolant	Removes heat from the reactor and transfers it to a generator (water or CO₂)
Shielding	Thick concrete and lead walls protect workers from radiation
Heat exchanger	Transfers heat from coolant to make steam that drives turbines to generate electricity

🧠 Control rods = brakes on the reaction. The more control rods pushed in, the more neutrons are absorbed, the slower the reaction. Pull them out = more neutrons = more fission = more energy (but dangerous if pulled out too fast — like Chernobyl!).

♻️ Advantages and Disadvantages

✅ Advantages

No greenhouse gases produced
Produces massive amounts of energy from small amounts of fuel
Reliable — not dependent on weather

❌ Disadvantages

Radioactive waste (dangerous for thousands of years)
Risk of accidents (e.g., Chernobyl, Fukushima)
Very expensive to build and decommission

Chapter 22 — Worked Examples

📐 Calculations: Chapter 22

Step-by-step worked examples for nuclear calculations.

🧮 Example 1 — Half-Life: Fraction Remaining

Q: Carbon-14 has a half-life of 5,730 years. How much of a sample remains after 11,460 years?

Step 1 — Find how many half-lives have passed

Number of half-lives = Time elapsed / Half-life = 11,460 / 5,730 = 2 half-lives

Step 2 — Apply the halving rule

After 1 half-life: ½ remains
After 2 half-lives: ½ × ½ = ¼ remains

✅ Answer: ¼ (one quarter) of the original sample remains

🧮 Example 2 — Decay Constant & Activity (HL)

Q: Carbon-14 half-life = 5,730 years. (i) Find the decay constant. (ii) Find the activity of a sample with 5.2 × 10¹¹ atoms.

Step 1 — Convert half-life to seconds

T½ = 5730 × 365 × 24 × 60 × 60 = 5730 × 3.156 × 10⁷ = 1.807 × 10¹¹ s

Step 2 — Find decay constant: λ = ln2 / T½ = 0.693 / T½

λ = 0.693 / (1.807 × 10¹¹) = 3.83 × 10⁻¹² s⁻¹

Step 3 — Find activity: A = λN

A = (3.83 × 10⁻¹²) × (5.2 × 10¹¹)
A ≈ 2.0 Bq

✅ λ = 3.83 × 10⁻¹² s⁻¹, Activity = 2.0 Bq (2 decays per second)

🧮 Example 3 — E = mc² Calculation

Q: 80 MJ of energy are released in a nuclear reaction. Calculate the loss of mass. (c = 3 × 10⁸ m/s)

Step 1 — Convert energy to joules

E = 80 MJ = 80 × 10⁶ J = 8 × 10⁷ J

Step 2 — Rearrange E = mc² for mass

m = E / c² = (8 × 10⁷) / (3 × 10⁸)²
m = (8 × 10⁷) / (9 × 10¹⁶)
m = 8.89 × 10⁻¹⁰ kg

✅ Mass lost = 8.89 × 10⁻¹⁰ kg (less than a millionth of a gram, yet produces 80 million joules!)

🧮 Example 4 — Completing a Nuclear Equation

Q: Complete this alpha decay equation: ²²⁶₈₈Ra → ??? + ⁴₂He

Step 1 — Find mass number of daughter nucleus

226 = A + 4 → A = 226 − 4 = 222

Step 2 — Find atomic number of daughter nucleus

88 = Z + 2 → Z = 88 − 2 = 86

Step 3 — Look up element with Z=86 (Radon = Rn)

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

✅ Radium-226 decays to Radon-222 by alpha emission

Chapter 22 — Quiz

✅ Quiz: Chapter 22

Test yourself on The Nucleus!

📋 All Formulas — Quick Reference

Every formula you need for the Modern Physics Leaving Cert exam. Learn these off!

Chapter 21 — The Electron

Energy of a charged particle in electric field

E = qV

E=energy (J), q=charge (C), V=voltage (V)

Energy conversion — potential to kinetic

qV = ½mv²

q=charge, V=voltage, m=mass, v=velocity

Convert eV to Joules

E(J) = E(eV) × 1.6 × 10⁻¹⁹

Force on charged particle in magnetic field

F = qvB

F=force (N), q=charge (C), v=velocity (m/s), B=magnetic flux density (T)

Energy of a photon

E = hf

E=energy (J), h=Planck's constant=6.6×10⁻³⁴ Js, f=frequency (Hz)

⭐ Einstein's Photoelectric Equation (HL)

hf = Φ + ½mv²_max

hf=photon energy, Φ=work function, ½mv²=KE of electron

Work Function

Φ = hf₀

Φ=work function (J), f₀=threshold frequency (Hz)

Chapter 22 — The Nucleus

Emission line spectra

hf = E₂ − E₁

Energy of photon emitted = difference between energy levels

Mass-energy equivalence

E = mc²

E=energy (J), m=mass (kg), c=3×10⁸ m/s

⭐ Law of Radioactive Decay (HL)

A = λN

A=activity (Bq), λ=decay constant (s⁻¹), N=number of undecayed nuclei

⭐ Half-life & Decay Constant (HL)

T½ = ln2/λ = 0.693/λ

T½=half-life (s), λ=decay constant (s⁻¹)

Planck's constant

h = 6.6×10⁻³⁴ Js

Electron charge

e = 1.6×10⁻¹⁹ C

Electron mass

m = 9.1×10⁻³¹ kg

Speed of light

c = 3×10⁸ m/s

⭐ Higher Level only formulas are marked with a star. Ordinary Level students don't need those ones! All others are needed by everyone.

📖 All Definitions — Learn These Off!

These are the definitions you need to be able to write in the exam. Learn them word-for-word!

Chapter 21 — The Electron

Electron

An electron is an indivisible quantity of charge that orbits the nucleus of an atom.

Electronvolt (eV)

The electronvolt is the energy gained or lost by an electron when it moves through a potential difference of 1 volt. 1 eV = 1.6 × 10⁻¹⁹ J.

Thermionic Emission

Thermionic emission is the emission of electrons from the surface of a hot metal.

Work Function (Φ)

The work function of a metal is the minimum energy needed to remove the loosest electrons from the surface of that metal.

X-Rays

X-rays are electromagnetic radiation of extremely high frequency (short wavelength).

Photoelectric Effect

The photoelectric effect is the emission of electrons from the surface of a metal due to electromagnetic radiation of a suitable frequency hitting the metal.

Photon

A photon is a bundle (packet) of light energy.

Threshold Frequency (f₀)

The threshold frequency is the minimum frequency of electromagnetic radiation needed to cause photoelectric emission from a given metal.

Einstein's Photoelectric Law (HL)

The energy of the fastest emitted electron equals the difference between the energy of the photon and the work function of the metal.

Chapter 22 — The Nucleus

Isotopes

Isotopes are atoms of the same element (same number of protons) but with different numbers of neutrons (different mass numbers).

Radioactivity

Radioactivity is the spontaneous emission of radiation due to the natural disintegration of an unstable nucleus.

Radiation

Radiation is the emission of particles of matter or photons of energy from a nucleus.

Alpha Emission (α)

Alpha emission is the emission of a helium nucleus (²He) from a large, unstable atom.

Beta Emission (β)

Beta emission is the emission of an electron when a neutron decays into a proton inside the nucleus.

Ionisation

Ionisation is the charging of a neutral atom or molecule when it loses or gains one or more electrons.

Penetration

Penetration is the distance radiation travels through a medium.

Background Radiation

Background radiation is radiation that comes from environmental sources including the Earth's crust, the atmosphere, cosmic rays, and radioisotopes.

Half-Life (T½)

The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.

Activity (A)

The activity of a radioactive source is the number of decays (disintegrations) per second. Unit: becquerel (Bq).

Decay Constant (λ) (HL)

The decay constant is the probability that an individual nucleus will decay in one second.

Nuclear Fission

Nuclear fission is the splitting of a large nucleus into two smaller nuclei (of roughly equal mass), with the emission of neutrons and release of energy.

Chain Reaction

A chain reaction is a reaction where at least one neutron is released during each fission reaction, causing further fissions — it is self-sustaining.

Critical Mass

Critical mass is the minimum amount of fissile material needed for chain reactions to occur.

Nuclear Fusion

Nuclear fusion is the combining of two small nuclei to form a single larger nucleus, with the release of energy.

🎯 Exam tip: For definitions, use the exact wording above. Examiners are looking for key words like "spontaneous", "minimum frequency", "indivisible", etc. Missing one key word can cost you marks!