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 Length
Length/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 mass
Mass/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 time
Time/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 prefixes
Power
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?