ORDERS OF
MAGNITUDE
The ‘mole’
- ‘One mole’ of a substance has 6 x 1023 molecules
in it. (This number is called Avogadro’s constant)
- So a chemist may measure out 3 moles of sulphur
and she would know that she has 18 x 1023
molecules of sulphur.
-She could also estimate that she has roughly 1024
molecules of sulphur.
1.1 The Realm of Physics
Q1. How many molecules are there in the Sun?
Info: - Mass of Sun = 1030 kg
- Assume it is 100% Hydrogen
- Avogadro constant = No. of molecules
in one mole of a substance = 6 x 1023
- Mass of one mole of Hydrogen = 2g
A.
Mass of Sun = 1030 kg x 1000g/kg = 1033 g
No. of moles of Hydrogen in Sun = 1033 g/ 2 g/mol
= 5 x 1032mol
No. of molecules in Sun
= ( 6 x 1023 molecules/mol) x ( 5 x 1032 mol)
= 3 x 1056 molecules
Orders of Magnitude
Orders of magnitude are numbers on a scale where
each number is rounded to the nearest power of
ten. This allows us to compare measurements,
sizes etc.
E.g. A giraffe is about 6m tall. So to the nearest power of
ten we can say it is 10m = 1x101m = 101m tall.
An ant is about 0.7mm tall. So to the nearest power of
ten we can say it is 1mm = 1x10-3m = 10-3m tall.
So if an ant is 10-3m tall and the giraffe 101m tall, then
the giraffe is bigger by four orders of magnitude.
Orders of magnitude link
Order of Magnitude of some Masses
Order of Magnitude of some Lengths
MASS
LENGTH
grams
meters
electron
10-27
diameter of nucleus
10-15
proton
10-24
diameter of atom
10-10
virus
10-16
radius of virus
10-7
amoeba
10-5
radius of amoeba
10-4
raindrop
10-3
height of human being
100
ant
100
radius of earth
107
human being
105
radius of sun
109
pyramid
1013
earth-sun distance
1011
earth
1027
radius of solar system
1013
sun
1033
distance of sun to nearest
star
1016
milky way galaxy
1044
radius of milky way galaxy
1021
the Universe
1055
radius of visible Universe
1026
Q2. There are about 1x1028 molecules of air in the
lab. So by how many orders of magnitude are
there more molecules in the Sun than in the lab?
From Q1, we found about 1056 molecules in the sun
so:
A. 1056 / 1028 = 1028 so 28 orders of magnitude
more molecules in the Sun.
Q3. Determine the ratio of the diameter of a
hydrogen atom to the diameter of a hydrogen
nucleus to the nearest order of magnitude.
A. Ratio = 10-10 / 10-15 = 105
Fermi Question: How many atoms would fit
along the Earth’s radius?
Answer:
107/10-10 = 1017