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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 road (not highway) 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 6,7 in your online notes.