Some nuclei are unstable and throw out particles or energy at random. The pattern of that decay is predictable even though no single decay is.
☢️ Alpha, beta and gamma
Alpha (α): a helium nucleus (2 protons, 2 neutrons); strongly ionising; stopped by paper or a few centimetres of air. Beta (β): a fast electron from the nucleus; stopped by a few millimetres of aluminium. Gamma (γ): electromagnetic radiation; weakly ionising; reduced by thick lead or concrete.
alpha decay: mass number −4, atomic number −2
U-238 (92) → Th-234 (90) + α
beta decay: mass number same, atomic number +1
Background radiation comes from rocks, cosmic rays and food. Always subtract it from a measured count rate.
🖼️ See it
The more strongly a radiation ionises, the less far it penetrates.Every 3 hours the count rate halves, however much sample is left.
⏳ Half-life
The half-life is the time for half the radioactive nuclei in a sample to decay (or for the count rate to halve). It is constant for each isotope, whatever the amount.
half-life 8 days, 80 g sample
8 days: 40 g
16 days: 20 g
24 days: 10 g
count rate 400 counts/min, half-life 3 h
after 6 h (2 half-lives): 100 counts/min
✏️ Quick check · 1 of 8
Penetration
Which radiation is stopped by a sheet of paper?
The least penetrating.
✏️ Quick check · 2 of 8
What is gamma?
Gamma radiation is:
No mass, no charge.
✏️ Quick check · 3 of 8
Half-life
The half-life of an isotope is the time for:
Half of the sample.
✍️ Type your answer · 4 of 8
Uranium-238 (mass number 238) undergoes alpha decay.
What is the mass number of the new nucleus?
Enter an exact answer, without rounding.
Alpha removes 4 nucleons.
✍️ Type your answer · 5 of 8
Uranium-238 (atomic number 92) undergoes alpha decay.
What is the atomic number of the new nucleus?
Enter an exact answer, without rounding.
Alpha removes 2 protons.
✍️ Type your answer · 6 of 8
A 80 g sample has a half-life of 8 days.
What mass remains after 24 days, in g?
Enter an exact answer, without rounding.
g
Halve it three times.
✍️ Type your answer · 7 of 8
A source has a count rate of 400 counts/min and a half-life of 3 hours.
What is the count rate after 6 hours, in counts/min?
Enter an exact answer, without rounding.
counts/min
Halve it twice.
✍️ Type your answer · 8 of 8
Measured count rate is 52 counts/min and background is 12 counts/min.
What is the corrected count rate, in counts/min?
Enter an exact answer, without rounding.
counts/min
Subtract the background.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
Which particle consists of 2 protons and 2 neutrons?
Question 2 of 5
Beta decay changes the atomic number by:
Question 3 of 5
After 3 half-lives, the fraction of the sample remaining is:
Question 4 of 5
Which radiation is most penetrating?
Question 5 of 5
Radioactive decay is:
Lesson 2 · Space
🪐 Space Physics: Orbits, Red-Shift & the Big Bang
Gravity holds planets, moons and satellites in orbit. Light from distant galaxies tells us the Universe is expanding.
🛰️ Orbits
An object stays in a circular orbit because gravity provides the centripetal force, constantly pulling it towards the centre. The speed of an orbiting object is orbital speed = circumference ÷ orbital period (v = 2πr ÷ T). The larger the orbit, the slower the speed and the longer the period.
Moon: light takes 1.3 s to reach the Earth
distance = 300 000 km/s × 1.3 s = 390 000 km
circular orbit of length 42 000 km in 6 h
speed = 42 000 ÷ 6 = 7000 km/h
🖼️ See it
The straight line shows speed proportional to distance, with gradient H₀ ≈ 70 km/s per Mpc. This is evidence that the Universe is expanding.
🌌 Red-shift and the Big Bang
Light from distant galaxies is red-shifted: its wavelength is stretched because the galaxy is moving away. The further away a galaxy, the bigger the red-shift and the faster it recedes. Hubble’s law: v = H₀ × d, with H₀ ≈ 70 km/s per megaparsec. The Universe began in a hot, dense state about 13.8 billion years ago and has been expanding since: the Big Bang. The cosmic microwave background is its leftover radiation.
galaxy 100 Mpc away: v = 70 × 100 = 7000 km/s
✏️ Quick check · 1 of 8
Centripetal force
What provides the centripetal force for a planet orbiting the Sun?
The attractive force.
✏️ Quick check · 2 of 8
Orbits
Compared with a close planet, a distant planet orbits with:
Farther means slower.
✏️ Quick check · 3 of 8
Red-shift
Red-shift of light from a galaxy tells us the galaxy is:
Longer wavelengths.
✏️ Quick check · 4 of 8
Evidence
Which is evidence for the Big Bang?
Leftover radiation.
✍️ Type your answer · 5 of 8
Light from the Moon takes 1.3 s to reach the Earth (c = 300 000 km/s).
What is the Earth–Moon distance, in km?
Enter an exact answer, without rounding.
km
distance = speed × time.
✍️ Type your answer · 6 of 8
A satellite orbit has a length of 42 000 km and takes 6 hours.
What is its speed, in km/h?
Enter an exact answer, without rounding.
km/h
speed = distance ÷ time.
✍️ Type your answer · 7 of 8
Hubble’s law with H₀ = 70 km/s per Mpc.
How fast is a galaxy 100 Mpc away receding, in km/s?
Enter an exact answer, without rounding.
km/s
v = H₀ × d.
✍️ Type your answer · 8 of 8
A galaxy is 200 Mpc away (H₀ = 70 km/s per Mpc).
What is its recession speed, in km/s?
Enter an exact answer, without rounding.
km/s
v = H₀ × d.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
The Universe is thought to have begun with:
Question 2 of 5
A geostationary satellite has an orbital period of:
Question 3 of 5
Hubble’s law says recession speed is:
Question 4 of 5
Which is NOT part of the Solar System?
Question 5 of 5
Red-shift means the wavelength of light has become:
Lesson 3 · Forces
⚖️ Moments & Centre of Gravity
Why is a door handle far from the hinges? Why do racing cars sit so low? Turning effects and balance explain both.
🔧 Moments
The moment of a force measures its turning effect: moment = force × perpendicular distance from the pivot, in N m. The principle of moments says that when an object is balanced, the total clockwise moment equals the total anticlockwise moment.
20 N applied 0.5 m from a hinge
moment = 20 × 0.5 = 10 N m
See-saw: 300 N sits 2 m from the pivot
anticlockwise moment = 300 × 2 = 600 N m
to balance, 400 N must sit at 600 ÷ 400 = 1.5 m
Equilibrium needs two things: no resultant force and no resultant moment.
🖼️ See it
The see-saw balances because the two moments are equal.
🎯 Centre of gravity
The centre of gravity is the point where an object’s weight appears to act. An object is more stable with a low centre of gravity and a wide base. It topples when the line of its weight falls outside its base.
Finding it for a flat card:
1. Hang the card from a pin so it swings freely
2. Hang a plumb line from the pin and mark the vertical
3. Repeat from a different hole
4. The centre of gravity is where the lines cross
✏️ Quick check · 1 of 7
Definition
The moment of a force is:
Force and distance.
✏️ Quick check · 2 of 7
Unit
The unit of a moment is the:
Force unit × distance unit.
✏️ Quick check · 3 of 7
Door
A door handle is far from the hinges so that:
Moment = F × d.
✏️ Quick check · 4 of 7
Stability
Which design is the most stable?
Think of a racing car.
✍️ Type your answer · 5 of 7
A 40 N force acts 0.25 m from a pivot.
What is the moment, in N m?
Enter an exact answer, without rounding.
N m
Multiply.
✍️ Type your answer · 6 of 7
A beam balances. On one side, 30 N acts 0.4 m from the pivot. On the other, a force F acts 0.6 m from the pivot.
What is F, in N?
Enter an exact answer, without rounding.
N
Clockwise = anticlockwise.
✍️ Type your answer · 7 of 7
A 500 N child sits 1.2 m from a see-saw’s pivot. A 400 N child balances them.
How far from the pivot is the 400 N child, in m?
Enter an exact answer, without rounding.
m
Use the principle of moments.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
An object is in equilibrium when there is:
Question 2 of 5
The centre of gravity is the point where:
Question 3 of 5
A bus tilts until its weight’s line falls outside its base. It will:
Question 4 of 5
A longer spanner makes a nut easier to turn because it:
Question 5 of 5
To find a card’s centre of gravity, you hang it from two points and use a:
Lesson 4 · Nuclear physics
⚛️ The Nuclear Atom
A beam of alpha particles fired at thin gold foil changed what we know about atoms. Most passed straight through, but a few bounced back.
🔬 Inside the atom
An atom has a tiny, positively charged nucleus with negatively charged electrons in orbit around it. An atom becomes a positive ion by losing electrons and a negative ion by gaining them.
alpha scattering by thin metal foil
most pass straight through → the atom is mostly empty space
a few deflect strongly → the nucleus is positive
very few bounce back → the nucleus is tiny and has most of the mass
🖼️ See it
A neutral atom has equal numbers of protons and electrons.
🧮 Protons, neutrons and notation
The nucleus contains protons and neutrons. Relative charges are proton +1, neutron 0, electron −1. Proton number Z counts the protons. Nucleon number A counts protons and neutrons. Isotopes are atoms of the same element with different numbers of neutrons.
neutrons = A − Z
sodium-23, Z = 11: neutrons = 23 − 11 = 12
chlorine-35 and chlorine-37 are isotopes
both have Z = 17
neutrons: 18 and 20
💥 Fission and fusion
In nuclear fission, a large unstable nucleus splits into smaller nuclei, as in nuclear power stations. In nuclear fusion, small nuclei join to make a larger one, as in the Sun. Both release large amounts of energy.
Remember the words: fission splits, and fusion fuses.
✏️ Quick check · 1 of 8
Scattering
Most alpha particles pass straight through thin foil, which shows that the atom is:
Nothing got in the way.
✏️ Quick check · 2 of 8
Bouncing back
A few alpha particles bounce back. This shows that the nucleus:
What could stop them?
✏️ Quick check · 3 of 8
Charge
The relative charge of a neutron is:
The name is a clue.
✏️ Quick check · 4 of 8
Isotopes
Isotopes of an element have different numbers of:
The element stays the same.
✍️ Type your answer · 5 of 8
A nucleus has nucleon number 23 and proton number 11.
How many neutrons does it have?
Enter an exact answer, without rounding.
A − Z.
✍️ Type your answer · 6 of 8
Chlorine-37 has proton number 17.
How many neutrons does it have?
Enter an exact answer, without rounding.
A − Z.
✍️ Type your answer · 7 of 8
A neutral atom has 8 protons.
How many electrons does it have?
Enter an exact answer, without rounding.
The charges must balance.
✍️ Type your answer · 8 of 8
A magnesium atom has 12 electrons, and it loses 2 to form an ion.
How many electrons does the ion have?
Enter an exact answer, without rounding.
Subtract.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The nucleus of an atom is:
Question 2 of 5
An atom forms a positive ion by:
Question 3 of 5
The nucleon number counts:
Question 4 of 5
Energy in the Sun is released by:
Question 5 of 5
In a nuclear power station, energy is released by:
Lesson 5 · Light
🔦 Total Internal Reflection & Lenses
Optical fibres carry the internet as flashes of light. A camera, your eye and a magnifying glass all bend light on purpose.
💎 Total internal reflection
When light going from glass to air meets the surface at more than the critical angle, it all reflects back inside. This is total internal reflection, used in optical fibres. The refractive index is n = sin i ÷ sin r, and n = 1 ÷ sin c.
glass with n = 1.5
sin c = 1 ÷ 1.5 = 0.667
c ≈ 42°
incidence below c: most light refracts out
incidence above c: all light reflects inside
🔍 Thin lenses
A converging lens brings parallel rays to a point, the principal focus. The distance to it is the focal length. Images can be real (can be projected) or virtual (cannot). A diverging lens spreads rays out.
object beyond 2f: real, inverted, smaller (camera)
object between f and 2f: real, inverted, larger (projector)
object inside f: virtual, upright, larger (magnifying glass)
✏️ Quick check · 1 of 6
Condition
Total internal reflection needs light to be:
Glass to air.
✏️ Quick check · 2 of 6
Fibres
Optical fibres work by:
It stays inside.
✏️ Quick check · 3 of 6
Lens
A converging lens is used in a:
It enlarges small print.
✏️ Quick check · 4 of 6
Virtual
A virtual image:
Can you catch it on a screen?
✍️ Type your answer · 5 of 6
Light strikes a glass surface. n = 1.5 and sin r = 0.4.
What is sin i, as a decimal?
Enter an exact answer, without rounding.
Rearrange the formula.
✍️ Type your answer · 6 of 6
A material has a critical angle where sin c = 0.5.
What is its refractive index?
Enter an exact answer, without rounding.
n = 1 ÷ sin c.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
Above the critical angle, light in glass will:
Question 2 of 5
The focal length is the distance from the lens to the:
Question 3 of 5
A camera image of a distant object is:
Question 4 of 5
A magnifying glass forms an image that is:
Question 5 of 5
A higher refractive index means a:
Lesson 6 · Electricity
🔌 EMF, Resistance & Potential Dividers
Why does a street light come on at dusk? A clever pair of resistors can sense the dark.
🔋 EMF and p.d.
Electromotive force (e.m.f.) is the energy supplied by a source per unit charge, in volts. Potential difference (p.d.) is the energy transferred per unit charge between two points. R = V ÷ I. Resistance rises with length and falls with thicker wire.
series: R = R₁ + R₂
parallel: 1/R = 1/R₁ + 1/R₂
6 Ω and 3 Ω in parallel
1/R = 1/6 + 1/3 = 1/2
R = 2 Ω
⚖️ Potential dividers
Two series resistors share the supply voltage in the ratio of their resistances: V₁ / V₂ = R₁ / R₂. A thermistor’s resistance falls as it warms, and a light-dependent resistor (LDR)’s resistance falls in brighter light, so they make sensors.
12 V across 4 kΩ and 2 kΩ
V across 4 kΩ = 12 × 4/6 = 8 V
V across 2 kΩ = 12 × 2/6 = 4 V
✏️ Quick check · 1 of 6
EMF
E.m.f. is measured in:
The same unit as p.d.
✏️ Quick check · 2 of 6
LDR
In brighter light, an LDR’s resistance:
Light-dependent.
✏️ Quick check · 3 of 6
Thermistor
As a thermistor warms up, its resistance:
More charge carriers.
✍️ Type your answer · 4 of 6
A 6 Ω and a 3 Ω resistor are in parallel.
What is the combined resistance, in Ω?
Enter an exact answer, without rounding.
Ω
Add the reciprocals.
✍️ Type your answer · 5 of 6
A 12 V supply is across 4 kΩ and 2 kΩ in series.
What is the p.d. across the 4 kΩ resistor, in V?
Enter an exact answer, without rounding.
V
The larger resistor gets the larger share.
✍️ Type your answer · 6 of 6
A lamp carries 2 A when the p.d. across it is 12 V.
What is its resistance, in Ω?
Enter an exact answer, without rounding.
Ω
R = V ÷ I.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
In a series circuit, the current is:
Question 2 of 5
Two equal resistors in parallel have a total resistance that is:
Question 3 of 5
A longer wire of the same material has:
Question 4 of 5
A thicker wire has:
Question 5 of 5
A potential divider splits voltage by the ratio of its:
Lesson 7 · Practical skills
🔬 Experimental Skills
Cambridge sciences include a practical paper. Good scientists know their variables, repeat their readings and spot what went wrong.
🧪 Planning a fair experiment
The independent variable is what you change. The dependent variable is what you measure. Control variables are kept the same. Repeat readings to spot anomalies and find a mean.
How does length affect a pendulum’s swing time?
independent: length of string
dependent: time for 10 swings
control: mass, angle of release
repeat 3 times and take the mean
📊 Recording and graphing
In a table, put units in the headings and use consistent decimal places. On a graph, put the independent variable on the x-axis, label axes with units, plot points and draw a line of best fit. Timing 10 swings then dividing reduces timing errors.
mean of 12.1, 12.3, 12.2 = 36.6 ÷ 3 = 12.2 s
time for one swing = 12.2 ÷ 10 = 1.22 s
Evaluating: say what limited your accuracy and suggest a specific improvement, such as using light gates in place of a stopwatch.
✏️ Quick check · 1 of 6
Independent
The independent variable is the one you:
You choose its values.
✏️ Quick check · 2 of 6
Dependent
The dependent variable is the one you:
The result.
✏️ Quick check · 3 of 6
Repeat
Readings are repeated in order to:
What if one is odd?
✏️ Quick check · 4 of 6
Table
Units in a results table belong in the:
Top of each column.
✍️ Type your answer · 5 of 6
Three readings are 4.2 s, 4.4 s and 4.3 s.
What is the mean, in s?
Enter an exact answer, without rounding.
s
Add, then divide by 3.
✍️ Type your answer · 6 of 6
Ten swings of a pendulum take 15 s.
What is the time for one swing, in s?
Enter an exact answer, without rounding.
s
Divide by 10.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
An anomaly is a result that:
Question 2 of 5
Which goes on the x-axis?
Question 3 of 5
Timing 10 swings instead of 1 reduces the effect of:
Question 4 of 5
A line of best fit should:
Question 5 of 5
Which is a useful improvement to an experiment?
Final Challenge
🏆 18-Question Challenge Quiz
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
0 / 18
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · Radioactivity & Half-Life
A radioactive sample’s activity falls from 800 to 100 counts/min in 9 days. The half-life is:
Q2 · Radioactivity & Half-Life
80 g of a substance has a half-life of 5 days. After 15 days, what remains is:
Q3 · Radioactivity & Half-Life
Alpha radiation is stopped by:
Q4 · Radioactivity & Half-Life
Gamma radiation is:
Q5 · Space Physics: Orbits, Red-Shift & the Big Bang
The best evidence that the Universe is expanding is:
Q6 · Space Physics: Orbits, Red-Shift & the Big Bang
Red-shift in the light from distant galaxies shows they are:
Q7 · Space Physics: Orbits, Red-Shift & the Big Bang
The force that keeps a planet in orbit around the Sun is:
Q8 · Space Physics: Orbits, Red-Shift & the Big Bang
The cosmic microwave background radiation is evidence for:
Q9 · Moments & Centre of Gravity
A 60 N force acts 0.5 m from a pivot. The moment is:
Q10 · Moments & Centre of Gravity
Lowering a vehicle’s centre of gravity makes it:
Q11 · The Nuclear Atom
Uranium-235 has proton number 92. How many neutrons does it have?
Q12 · The Nuclear Atom
The alpha scattering experiment supported:
Q13 · Total Internal Reflection & Lenses
A diverging lens makes parallel rays:
Q14 · Total Internal Reflection & Lenses
Optical fibres are mainly used for:
Q15 · EMF, Resistance & Potential Dividers
A dusk light sensor is most likely to use a:
Q16 · EMF, Resistance & Potential Dividers
9 V across 1 kΩ and 2 kΩ in series. The p.d. across 2 kΩ is:
Q17 · Experimental Skills
Keeping the mass the same in a pendulum test makes it a: