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```IB DP Physics SL and HL
1.1.1 - 1.1.4
The Realm of Physics
By Navam Pakianathan
Introduction to Order of
Magnitude (OOM):
What is an order of magnitude?
OOM of a number is the (integral)
power of ten closest to that number.
For eg,
OOM of 1028 is 28
OOM of 2.43 x 1028 is 28
OOM of 6.84 x 1028 is 29
(6.84 x 1028  10 x 1028 = 1029)
How do we find OOM?
We round off to the nearest power of
ten, i.e. to ….1/1000, 1/100, 1/10,1,
10, 100, 1000, etc
When dealing with very big or very
small numbers, scientists are more
concerned with the OOM rather than
the precise value
Examples of finding order of
magnitude.
1. What is the speed of light?
Exact answer: 2.99979 x 108 ms-1
Difficult to remember!
Better remembered as 3 x 108 ms-1
Or even better as simply 108 ms-1 (since 3
is closer to 1 than to 10, we approximate
3 to 1. Thus 3 x 108 ms-1 = 108 ms-1
Here the ‘8’ is called an order of
magnitude
Examples of finding order of
magnitude.
1. What is the speed of light?
Exact answer: 2.99979 x 108 ms-1
Difficult to remember!
Better remembered as 3 x 108 ms-1
Or even better as simply 108 ms-1 (since 3
is closer to 1 than to 10, we approximate
3 to 1. Thus 3 x 108 ms-1 = 108 ms-1
Here the ‘8’ is called an order of
magnitude
Examples of finding order of
magnitude.
2. What is the mass of the earth?
Exact answer: 5.98 x 1024 kg
Difficult to remember!
Better remembered as 6 x 1024 kg
Or even better as simply 1025 kg (since 6
is closer to 10, we approximate 6 to 10.
Thus 10 x 1024 kg = 1025 kg
Here the ‘25’ is called an order of
magnitude
Examples of finding order of
magnitude.
3. What is the mass of the sun?
Exact answer: 1.99 x 1030 kg
Difficult to remember!
Better remembered as 2 x 1030 kg
Or even better as simply 1030 kg (since 2
is closer to 1, we approximate 2 to 1.
Thus 1 x 1030 kg = 1030 kg
Here the ‘30’ is called an order of
magnitude
Range of magnitudes of distances
Distances: from 10–15 m to 10+25 m
(sub-nuclear particles to extent of
the visible universe).
Range of magnitudes of masses
Masses: from 10–30 kg to 10+50 kg
(electron to mass of the universe).
Range of magnitudes of times
Times: from 10–23 s to 10+18 s
(passage of light across a
nucleus to the age of the universe).
Comparing orders of magnitude
Example 1:
The diameter of the earth Is 12800 km and
the length of a railway platform is 115 m.
Compare these two lengths.
Solution:
12800 km  10000 km (rounding off to the
nearest power of ten) = 104 km = 107 m
115 m  100 m = 102 m
Thus,
diameter of the earth/ length of a railway
platform = 107 m/102 m = 105
Comparing orders of magnitude
Example 2
How much more massive is the sun
than the earth?
Ans: 1030 kg/1025 kg
=105
The sun is more massive than the
earth by 5 orders of magnitude.
Comparing orders of magnitude
Example 3
How much larger is the diameter of a
Hydrogen atom as compared to its
nucleus?
Diameter of a Hydrogen atom  10-10 m
Diameter of a Hydrogen nucleus  10-15 m
(Remember the above data)
Thus,
Diameter of a Hydrogen atom/ Diameter
of a Hydrogen nucleus = 10-10 m/10-15 m
= 105
Estimation
• What is the meaning of estimation
Estimation is the rough calculation of the
value, number, quantity, or extent of
something.
• Why estimate?
In day to day life it may be necessary to
refer to lengths, masses and time in an
approximate manner. The exact values
may not be important. In these situations,
estimation helps us.
Estimation : Example 1
A.
B.
C.
D.
Estimate the mass of an apple
10-2 kg
10-1 kg
100 kg
101 kg
Solution:
B. 10-1 kg
Found by the process of elimination
Estimation: Example 2
A.
B.
C.
D.
Estimate the width of a domestic
10-1 m
100 m
101 m
102 m
Solution:
C.
101 m
Found by the process of elimination. Note that a
highway could be up to 100 m wide in some parts.
Estimation: Example 3
A.
B.
C.
D.
Estimate the amount of milk drunk in
one year if a person drinks one glass in a
day
101 mL
102 mL
103 mL
105 mL
Solution:
1 glass = 200 ml (approx)
365 days  365 x 200 mL = 73000 mL
= 100,000 mL = 105 mL
Class and Home work
How many molecules are there in the
sun? Read this example from the
textbook Physics for the IB diploma
by K.A. Tsokos pg 2
Complete problems from Tsokos pgs
6,7 : No 5,8,12
Workout problems 2,9,13,16,
17,18,24,25,27,33 from Tsokos pgs