The Realm of Physics

Orders of Magnitude

• When quantities are written to the nearest power of 10, the quantity is being expressed as an “order of magnitude”. Often, part of learning physics is to appreciate the order of magnitude of things – whether they are masses, times, distances, forces, or just pure numbers such as the number of times your heart will beat in your lifetime.

Range of LengthLength/m

Distance to the edge of the observable universe 1026

Diameter of the Milky Way galaxy 1021

Distance to the nearest star outside our solar system 1016

Diameter of solar system 1013

Distance to sun 1011

Diameter of Earth 107

Radius of Earth 107

Size of a cell 10-5

Size of a hydrogen atom 10-10

Size of a nucleus 10-15

Size of a proton 10-17

Range of massMass/Kg

The universe 1053

The Milky Way galaxy 1041

The sun 1030

The earth 1024

An apple 10-1

A raindrop 10-6

A bacterium 10-15

Smallest virus 10-21

A hydrogen atom 10-27

An electron 10-31

Range of timeTime/s

Age of the universe 1017

Age of the earth 1017

Time of travel by light to nearest star 108

One year 107

One day 105

Period of one heartbeat 100

Period of red light 10-15

Time of passage of light across a nucleus 10-24

Making approximations

• By using orders of magnitude, we can arrive at approximate solutions to questions like “how many times does your heart beat in your lifetime.

• Ie. We live approximately 102 years, each year contains approximately 107 seconds, and our heart beats about 1 time per second. So, your heart beats about 109 times in your lifetime.

A similar calculation

• Assuming your heart beats 1 time per second, how many times would it beat in 75 years?

Comparing quantities

• Quantities can be compared using order of magnitude.

• Ie ratio of the size of a hydrogen atom to the size of its nucleus is 105.

• What is the mass of our galaxy in terms of solar mass?

• How many hydrogen atoms does it take to make up the mass of the earth?

The SI system (metric system)

• In the SI system there are seven fundamental units.

(1)The meter (m) – the unit of distance(2)The kilogram (kg) – the unit of mass(3)The second (s) – the unit of time(4)The ampere (A) – the unit of electric current(5)The Kelvin (K) – the unit of temperature

Fundamental units continued

(6) The mole (mol) – the number of atoms that are present in 12 g of carbon-12. One mole of any substance contains 6.02 x 1023 “particles” of the substance.

(7) The candela (cd) – This is the unit of luminous intensity.

Derived units

• Physical quantities other than those listed above have units that are combinations of the seven fundamental units. Such units are called derived units.

• Ex. The unit of force is the Newton (N)• 1N = 1 kgms-2.

Common metric prefixes

Power Prefix Symbol

10-18 atto a

10-15 femto f

10-12 pico p

10-9 nano n

10-6 micro µ

10-3 milli m

10-2 centi C

10-1 deci d

Common metric prefixesPower Prefix Symbol

101 deka da

102 hecto h

103 kilo k

106 mega M

109 giga G

1012 tera T

1015 peta P

1018 exa E

Some questions

(1) How many meters are there in 5.3 nm?(2) How many meters are there in 2.4 Gm?(3) How many seconds are there in 24 ms?(4) How many seconds are there in 14 days?(5) What is the volume in m3 of a cube of side 2.8

cm?(6) What is the velocity of an electron in m/s that

covers a distance of 15.68 mm in 87.50 ns?