A LevelPhysicsAQARevision NotesMeasurements & Their ErrorsUse of SI Units & Their PrefixesEstimating Physical Quantities

Estimating Physical Quantities (AQA A Level Physics): Revision Note

Exam code: 7408

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Updated on

Orders of Magnitude

  • When a number is expressed to an order of 10, this is an order of magnitude

    • For example, the order of magnitude of 3 × 108 is 108

  • Orders of magnitude follow rules for rounding

    • The order of magnitude of 6 × 108 is 109, as the magnitude is rounded up

  • A quantity is one order of magnitude larger than another quantity if it is about ten times larger

    • Similarly, two orders of magnitude would be 100 times larger, or 102

  • In physics, it can be difficult to comprehend the size of quantities that are very large or very small

  • Expressing a quantity as an order of magnitude makes it easier to compare it with more familiar quantities

    • For example, the length of a football field is about 100 m, or ~ 102 m

    • The distance between the Earth and the Sun is 1.5 × 1011 m, or ~ 1011 m

    • The difference is 10 to the power of 11 over 10 squared = 109, or 9 orders of magnitude, which means 109 (a billion) football fields could fit between the Earth and the Sun

Comparison of distances

Quantity

Length / m

Order of magnitude / m

distance to the edge of the observable Universe

4.40 × 1026

1026

distance from Earth to Neptune

4.5 × 1012

1012

distance from London to Cape Town

9.7 × 106

107

length of a human

1.7

100

length of an ant

9 × 10−4

10−3

length of a bacteria cell

2 × 10−6

10−6

Worked Example

Estimate the order of magnitude of the following:

(a) The temperature of an oven (in Kelvin)

(b) The volume of the Earth (in m3)

(c) The number of seconds in a person's life if they live to be 95 years old

Answer:

(a) Estimate the temperature of an oven

  • A conventional oven works at ∼200 °C 

  • T (in K) = 200 + 273 = 473 K

  • This is equivalent to 4.73 × 102 K

  • The order of magnitude is ∼102 K

(b) Estimate the volume of the Earth 

  • The radius of the Earth is ∼6.4 × 106 m

  • The volume of a sphere is equal to:

    • V space equals space 4 over 3 straight pi r cubed

    • V space equals space 4 over 3 straight pi cross times open parentheses 6.4 cross times 10 to the power of 6 close parentheses cubed = 1.1 × 1021 m3

  • The order of magnitude is ∼1021 m3

(c) Estimate the number of seconds in 95 years

  • 1 year = 365 × 24 × 60 × 60 = 31 536 000 s

  • 95 years = 95 × 31 536 000 = 283 824 000 s

  • This is approximately 2.84 × 108 s

  • Therefore, the order of magnitude is ∼108 s

Estimating Physical Quantities

  • There are important physical quantities to learn in physics

  • It is useful to know these physical quantities, they are particularly useful when making estimates

  • A few examples of useful quantities to memorise are given in the table below (this is by no means an exhaustive list)

Common estimations

Quantity

Size

Mass of an adult person

70 kg

Mass of a car

1000 kg

Height of an adult person

2 m

Diameter of a hair

10-4 m

Diameter of an atom

10−10 m

Diameter of a nucleus

10−15 m

Wavelength of UV radiation

10 nm

Distance between Earth and Sun (1 AU)

1011 m

Mass of a hydrogen atom

10−27 kg

Seconds in 1 day

90 000 s

Seconds in 1 year

3 × 107 s

Speed of sound in air

300 m s−1

Power of a light bulb

60 W

Atmospheric pressure

105 Pa

Worked Example

Estimate the energy required for an adult man to walk up a flight of stairs.

Answer:

Step 1: Recall the equation for energy for gain in gravitational potential energy:

  • For a man of mass m to gain height h in a gravitational field of strength g, the energy E required to do so is:

increment E subscript p space equals space m g increment h

  • Here, g is approximately 10 N kg−1

Step 2: Estimate the mass and height

  • An adult person has a mass of approximately 70 kg

  • A flight of stairs gains around 3 m of height

1-1-estimating-physical-quantities-cie-new

Estimation of the adult man's mass and the height of the stairs

Step 3: Substitute these estimates into the equation:

  • The energy required for the man to walk up the stairs is approximately:

increment E subscript p space equals space 70 space cross times space 10 space cross times space 3 space equals space 2100 space straight J

Examiner Tips and Tricks

You will only ever be asked to estimate physical quantities that you are familiar with from your studies, or that can be estimated due to your everyday experience, such as the speed of a person walking (1 - 1.5 m/s).

The mark schemes for calculations involving estimates are normally quite generous and offer a range of values as the final answer to accommodate the range of acceptable values.

Many values are already given in your data booklet, which may not be given in the question, so make sure to check there too! 

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Author
Reviewer
Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

Caroline Carroll

Reviewer: Caroline Carroll

Expertise: Physics & Chemistry Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.