Estimates
— Physics · AS Level (7408) · "Physical Quantities & Measurements" add-on —
★ Exam Tip: Estimates come up often, but are worth ≤ 1 mark — never a whole question. Sir: "not the end of the world" if you forget one. A
full question will never depend only on an estimate. Some you must memorise; many you can work
out from things you already know.
1. Memorise or Work Out?
- Memorise (can't be derived): masses of everyday objects, densities of oil/mercury, speed of sound, speed of light in glass, hair thickness, typical slit/grating numbers, nucleus & atom size.
- Work out (formula + a number you know): kWh → J, sphere volume, athlete's speed & KE, wavelengths in 1 m, fringe separation, frequency from λ, carbon-atom mass.
- Papers may give an estimate you were never taught (grain of sand, coin…) → just have a rough idea of its size / mass.
Data sheets — what you get in the exam: two printed sheets come
with the paper (not a separate booklet). One has constants (g, c, e …) and one has formulas.
For AS only a short formula list is printed; the next sheet (A2) is full. Not every formula is
given — learn the rest. Constants don't need memorising. (Chemistry gives everything; Physics does
not have its own stand-alone booklet.)
2. Typical Masses
| Object | Estimate | Sir's way to remember |
|---|---|---|
| Apple | 200 – 250 g | 1 kg of apples ≈ 5 apples (sometimes 4) ⇒ 1000÷5 = 200 g, 1000÷4 = 250 g |
| Protractor | 5 – 10 g | lighter than a coin-ish; very light |
| 30 cm ruler | ≤ 20 g | heavier than protractor, but never more than 20 g |
| Scientific calculator | 80 – 100 g | memorise |
| Cell phone | 60 – 100 g | about as heavy as a calculator, never more |
| Coin | ≈ 1 g (0.5 – 5 g) | not more than ~5 g, not much less than 0.5 g |
| Grain / speck of sand | ≈ 0.01 g | definitely < 0.1 g |
| Typical human / athlete | 60 – 80 kg | (60, 80, up to ~90) — an Olympic athlete is never heavier |
| 1 litre of water | 1 kg (1000 g) | 1 L = 1000 cm³ (O-level) × 1 g/cm³ ⇒ 1000 g |
| Carbon atom | ≈ 2 × 10⁻²⁶ kg | work out: 12 u × 1.66 × 10⁻²⁷ (see §7) |
Sir's trick: ruler → protractor → coin: all small ⇒ stay in grams.
Calculator & phone ≈ the same (tens of g).
Best way to remember 1 litre: 1 L = 1000 cm³, and water is 1 g per cm³ ⇒ 1000 cm³ → 1000 g = 1 kg. Remember 1 L = 1000 cm³ — more useful than remembering "1 kg".
3. Densities, Pressure & Speeds
| Quantity | Value | Note |
|---|---|---|
| Density of water | 1000 kg m⁻³ = 1 g cm⁻³ | learn either form — very handy |
| Density of oil | ≈ 800 kg m⁻³ | must memorise (less than water) |
| Density of mercury | 13 400 – 13 600 kg m⁻³ | memorise |
| Density of air (RTP) | 1.2 kg m⁻³ (≈ 1) | room temperature & pressure |
| Speed of sound in air | 330 m s⁻¹ (330 – 340) | "every child knows it" |
| Speed of sound in water | 1500 m s⁻¹ | memorise |
| Speed of sound in metals | 4000 – 5000 m s⁻¹ | memorise |
| Speed of light in glass | 2 × 10⁸ m s⁻¹ | (c in vacuum = 3 × 10⁸, given) |
| Young modulus of metals | 10¹⁰ – 10¹² Pa | metals barely stretch ⇒ very high E |
Order to remember (speed of sound): air 330 < water 1500 <
metal 4000–5000 m/s. Solids are fastest.
Pressure under water
Rule: pressure increases with depth — at each extra 10 m of water you add a fixed amount to the atmospheric pressure at the surface.
⚠ Discrepancy: in the lecture sir counted +2 atm per 10 m (1 → 3 → 5 atm). That doesn't match the physics, so the figure shows the checked value ↓
p = ρgh
p = 1000 × 9.81 × 10
p ≈ 1 × 10⁵ Pa ≈ 1 atm
so total at 10 m = 1 (air) + 1 (water) = 2 atm — double-check this with sir.
4. Sizes & Lengths
| Object | Estimate | How |
|---|---|---|
| Diameter of a nucleus | 10⁻¹⁴ – 10⁻¹⁵ m | memorise |
| Diameter of an α-particle | 10⁻¹⁴ – 10⁻¹⁵ m | an α is a helium nucleus ⇒ same as nucleus |
| Diameter of an atom | ≈ 10⁻¹⁰ m | obviously bigger than the nucleus (lecture garbled: sir said 10⁻¹⁰ to 10⁻¹²) |
| Diameter of a hair | 0.1 mm or 0.05 mm | hold a hair against a ruler — it doesn't even fill 1 mm |
| Volume of a human head | 1800 – 2500 cm³ | work out: sphere with r ≈ 8 cm (§7) |
Learn this: just memorise nucleus and atom sizes — don't
try to link them to γ-radiation / radioactivity; sir dropped that explanation. α-particle comes free from the
nucleus.
The recording is unclear on the exact atom range (10⁻¹⁰ / 10⁻¹¹ / 10⁻¹² were all said) — use ≈ 10⁻¹⁰ m, the standard value, and check it against your own sheet.
5. EM Waves & Visible Light
Idea: half of all the estimates are from the electromagnetic spectrum chapter — you already know the wavelengths, so find frequency from the wave equation.
v = fλ ⇒ f = vλ with v = c
= 3 × 10⁸ m s⁻¹
| Radiation / colour | Wavelength | Comment |
|---|---|---|
| Red light (vacuum) | ≈ 700 nm (680 – 700) | memorise what sir dictated |
| Green light | ≈ 550 nm | average of visible light |
| Blue / violet light | ≈ 450 nm | violet is very close to blue |
| Infrared | 10⁻³ – 10⁻⁶ m | already learnt in the EM-spectrum chapter |
| Ultraviolet | 10⁻⁶ – 10⁻⁸ m (board) | as sir gave it; note on longest λ ↓ |
| Radio waves, X-rays | — | use the EM-spectrum values already learnt; frequency from f = c/λ |
UV longest wavelength: sir noticed his working used the 10⁻⁸ end and
said he'd fix it later. The longest wavelength is the 10⁻⁶ m end, so use that ⇒ f =
3×10⁸ ÷ 10⁻⁶ = 3 × 10¹⁴ Hz.
Infrared → f range
f = c/λ
f = 3×10⁸ / 10⁻³ = 3×10¹¹ Hz
f = 3×10⁸ / 10⁻⁶ = 3×10¹⁴ Hz
UV (longest λ)
f = c/λ
f = 3×10⁸ / 10⁻⁶
f = 3×10¹⁴ Hz
How many wavelengths of visible light fit in 1 m?
Green is the average wavelength of visible light ⇒ number in 1 m = 1 m ÷ λgreen. Answer order: ~10⁶. Sir hasn't seen this worded in a real paper — just a possible estimate.
N = 1 mλ
N = 1550 × 10⁻⁹
N ≈ 1.8 × 10⁶ ≈ 10⁶
6. Double Slit & Diffraction Grating
From the Superposition chapter — memorise these typical values:
| Quantity | Typical value |
|---|---|
| Slit-to-screen distance D | 1 – 3 m (always metres, not cm) |
| Slit separation a | 0.5 – 1 mm (good average) |
| Fringe separation x | from x = λD/a, or memorise |
| Lines per mm on a grating | 500 – 2000 per mm |
If you can't recall x: take λ = 550 nm (green average), D = 1 m, a = 0.5 mm and substitute.
x = λDa
x = λDa
x = 550×10⁻⁹ × 10.5×10⁻³
x ≈ 1.1 × 10⁻³ m ≈ 1 mm
Careful with the grating units! 500–2000 lines are per mm, not
per m. To convert to per metre: 1 mm = 1 × 10⁻³ m, so multiply by 10³. 500 /mm → 5×10⁵
/m; 2000 /mm → 2×10⁶ /m.
7. Work-It-Out Estimates
Rule: sir has done the working for these — don't memorise the answers, just remember which base fact to start from.
① Joules in 1 kWh
1 kW = 1000 W
1 h = 60 × 60 s = 3600 s
E = 1000 × 3600
1 kWh = 3.6 × 10⁶ J
② Mass of a carbon atom
carbon-12 → 12 u
m = 12 × 1.66 × 10⁻²⁷
m ≈ 1.99 × 10⁻²⁶ kg
③ Volume of a human head (cm³)
Don't memorise it: measure with a ruler — head radius ≈ 8 cm (everyone's is close; 8–10 cm). Treat the head as a sphere.
V = 43πr³
V = 43π(8)³
V ≈ 2100 cm³
Check: r = 8 cm gives ≈ 2.1 × 10³
— inside sir's 1800–2500 band. r = 10 cm would give ≈ 4.2 × 10³ (outside), so stick with r ≈ 8 cm.
④ Olympic sprinter (100 m race)
Usain Bolt's record 9.58 s → call it ≈ 10 s (others 10 – 10.5 s). Typical mass of athlete: 60 – 80 kg.
Speed
v = dt
v = 10010
v ≈ 10 m s⁻¹
Kinetic energy
KE = 12mv²
KE = ½ × 60 (to 80) × 10²
KE ≈ 3000 – 4000 J
Note: sir said "½mv" in the lecture — it's of course ½mv².
Mass 60 → 3000 J; mass 80 → 4000 J.
⑤ Appliances (household power)
Look at the label on a bulb: 240 V, 1 A ⇒ P = VI = 240 × 1 = 240 W. Bulbs of ~240 W or 300 W are the sort of thing sir quoted. Rough general idea only — not a precise "must-learn".
Think "scale": unfamiliar item in an exam? Compare it with something
you know (coin, ruler, protractor, calculator) and give a sensible order of magnitude.
8. Don't Waste Time On These
- Skip — "speed of light in any medium": useless, never comes.
- Skip — refractive index of glass and of diamond ("never comes — don't know why it's listed").
- Skip — number of particles in 1 mole: it's in the data sheet (and covered properly in A2).
- Skip — the "wavelength of X-rays / infrared / radio" memorising: you already did these in EM spectrum.
Exam note: estimates are ≤ 1 mark each. Not knowing one is not fatal,
and a whole question will never depend on one.
9. Full Cheat-Sheet
✓ Memorise-These (values)
- Masses: apple 200–250 g · protractor 5–10 g · 30 cm ruler ≤ 20 g · calculator 80–100 g · phone 60–100 g · coin ≈ 1 g (0.5–5) · sand speck ≈ 0.01 g · human / athlete 60–80 kg · 1 L water = 1 kg (1 L = 1000 cm³)
- Densities: water 1000 kg m⁻³ (1 g cm⁻³) · oil 800 · mercury 13 400–13 600 · air 1.2
- Speeds: sound in air 330 (–340) · water 1500 · metals 4000–5000 m s⁻¹ · light in glass 2×10⁸ m s⁻¹
- Sizes: nucleus & α-particle 10⁻¹⁴–10⁻¹⁵ m · atom ≈ 10⁻¹⁰ m · hair 0.1 or 0.05 mm
- Light λ: red 700 (680) nm · green 550 nm (average) · blue/violet 450 nm · IR 10⁻³–10⁻⁶ m · UV 10⁻⁶–10⁻⁸ m
- Waves: D (slits→screen) 1–3 m · a (slit sep.) 0.5–1 mm · grating 500–2000 lines per mm · Young modulus of metals 10¹⁰–10¹² Pa
✓ Work-Out Formulas
- f = c/λ (c = 3×10⁸) | N in 1 m = 1 / λgreen ≈ 1.8×10⁶
- 1 kWh = 1000 × 3600 = 3.6×10⁶ J | carbon atom = 12 × 1.66×10⁻²⁷ = 1.99×10⁻²⁶ kg
- Head: V = 4/3 πr³ with r ≈ 8 cm ⇒ ≈ 2100 cm³ | Sprinter: v = 100/10 = 10 m s⁻¹, KE = ½mv² ≈ 3000–4000 J
- Fringe separation x = λD/a ≈ 550×10⁻⁹ × 1 / 0.5×10⁻³ ≈ 1 mm | Grating: ×10³ to convert /mm → /m
- Pressure under water: p = ρgh ≈ 1×10⁵ Pa (≈ 1 atm) per 10 m | (sir counted 2 atm per 10 m — check)
★ Final Exam Tip: not on the data sheet: most formulas — so learn
them. On the sheet: constants (g, c, e …). Estimates ≤ 1 mark, but some are easy marks — learn
the memorise list, derive the rest.