Orders of Magnitude and Units

The ‘mole’: - The amount of a substance can be described using ‘moles’. - ‘One mole’ of a substance has 6 x molecules in it. (This number is called the Avogadro constant) - So a chemist may measure out 3 moles of sulphur and she would know that she has 18 x molecules of sulphur.

1.1 The Realm of Physics Q1. How many molecules are there in the Sun? Info:- Mass of Sun = kg - Assume it is 100% Hydrogen - Avogadro constant = No. of molecules in one mole of a substance = 6 x Mass of one mole of Hydrogen = 2g A. Mass of Sun = x 1000 = g No. of moles of Hydrogen in Sun = / 2 = 5 x No. of molecules in Sun = ( 6 x ) x ( 5 x ) = 3 x molecules

Order of magnitude The number of atoms in 12g of carbon is approximately We can say to the nearest order of magnitude that the number of atoms in 12g of carbon is (6 x is 1 x to one significant figure) This can be written as 6 x 10 23

Small numbers Similarly the length of a virus is 2.3 x m. We can say to the nearest order of magnitude the length of a virus is m.

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 = 1x10 1 m = 10 1 m tall. An ant is about 0.7mm tall. So to the nearest power of ten we can say it is 1mm = 1x10 -3 m = m tall. So if an ant is m tall and the giraffe 10 1 m tall, then the giraffe is bigger by four orders of magnitude.

Orders of magnitude link

Ranges of sizes, masses and times You need to have an idea of the ranges of sizes, masses and times that occur in the universe.

Order of Magnitude of some Masses Order of Magnitude of some Lengths MASS grams LENGTH meters electron diameter of nucleus proton diameter of atom virus radius of virus amoeba10 -5 radius of amoeba raindrop10 -3 height of human being 10 0 ant10 0 radius of earth 10 7 human being10 5 radius of sun 10 9 pyramid10 13 earth-sun distance earth10 27 radius of solar system sun10 33 distance of sun to nearest star milky way galaxy10 44 radius of milky way galaxy the Universe10 55 radius of visible Universe 10 26

You have to LEARN these! Size m to m (subatomic particles to the extent of the visible universe) Mass kg to kg (electron to the mass of the Universe) Time s to s (time for light to cross a nucleus to the age of the Universe)

Q2. There are about 1x10 28 molecules of air in the lab. So by how many orders of magnitude are there more molecules in the Sun than in the lab? A / = so 28 orders of magnitude more molecules in the Sun.

A common ratio – Learn this! Q3. Determine the ratio of the diameter of a hydrogen atom to the diameter of a hydrogen nucleus to the nearest order of magnitude. Hydrogen atom ≈ m Proton ≈ m Ratio of diameter of a hydrogen atom to its nucleus = / = 10 5

Estimation For IB you have to be able to make order of magnitude estimates.

Estimate the following: 1.The mass of an apple (to the nearest order of

Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. (to the nearest order of)

Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. (to the nearest order of

Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. 4.The number of times the earth will fit into the sun (R s = 6.96 x 10 8, R e = 6.35 x 10 6 ) (to the nearest order of

Estimate the following: 1.The mass of an apple 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. 4.The number of times the earth will fit into the sun (R s = 6.96 x 10 8, R e = 6.35 x 10 6 ) 5.The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of)

Estimate the following: 1.The mass of an apple kg 2.The number of times a human heart beats in a lifetime. 3.The speed a cockroach can run. 4.The number of times the earth will fit into the sun (R s = 6.96 x 10 8, R e = 6.35 x 10 6 ) 5.The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of

Estimate the following: 1.The mass of an apple kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70= The speed a cockroach can run. 4.The number of times the earth will fit into the sun (R s = 6.96 x 10 8, R e = 6.35 x 10 6 ) 5.The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of)

Estimate the following: 1.The mass of an apple kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70= The speed a cockroach can run m/s 4.The number of times the earth will fit into the sun (R s = 6.96 x 10 8, R e = 6.35 x 10 6 ) 5.The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of)

Estimate the following: 1.The mass of an apple kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70= The speed a cockroach can run m/s 4.The number of times the earth will fit into the sun (6.96 x 10 8 ) 3 /(6.35 x 10 6 ) 3 = The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of)

Estimate the following: 1.The mass of an apple kg 2.The number of times a human heart beats in a lifetime. 70x60x24x365x70= The speed a cockroach can run m/s 4.The number of times the earth will fit into the sun (6.96 x 10 8 ) 3 /(6.35 x 10 6 ) 3 = The number of classrooms full of diet Pepsi Mrs Bright will drink in her lifetime. (to the nearest order of)

Prefixes PowerPrefixSymbol petaP terraT 10 9 gigaG 10 6 megaM 10 3 kilok PowerPrefixSymbol femtof picop nanon microµ millim

Prefixes Power Prefix Symbol attoa10 1 dekada femtof10 2 hectoh picop10 3 kilok nanon10 6 megaM microμ10 9 gigaG millim10 12 teraT centic10 15 petaP decid10 18 exaE Don’t worry! These will all be in the formula book you have for the exam.

Quantities and Units A physical quantity is a measurable feature of an item or substance. A physical quantity will have a value and usually a unit. (Note: Some quantities such as ‘strain’ are dimensionless and have no unit). E.g. A current of 5.3A ; A mass of 1.5x10 8 kg

The SI system of units There are seven fundamental base units which are clearly defined and on which all other derived units are based: You need to know these

Base quantities The SI system of units starts with seven base quantities. Base quantityBase UnitAbbreviation Base quantityBase UnitAbbreviation mass (m) Length (l) time (t) temperature (T) electric current (I) amount of substance (n) luminous intensity (I v ) Base quantityBase UnitAbbreviation mass (m)kilogramkg Length (l)metrem time (t)seconds temperature (T)KelvinK electric current (I)AmpereA amount of substance (n)molemol luminous intensity (I v )candelacd

SI Base Units QuantityUnit distancemetre timesecond currentampere temperaturekelvin quantity of substancemole luminous intensitycandela masskilogram Can you copy this please ? Note: No Newton or Coulomb

Derived units Other physical quantities have units that are combinations of the fundamental units. Speed = distance/time = m.s -1 Acceleration = m.s -2 Force = mass x acceleration = kg.m.s -2 (called a Newton) (note in IB we write m.s -1 rather than m/s)

Some important derived units (learn these!) 1 N = kg.m.s -2 (F = ma) 1 J = kg.m 2.s -2 (W = Force x distance) 1 W = kg.m 2.s -3 (Power = energy/time) Gue ss what

Derived units The seven base units were defined arbitrarily. The sizes of all other units are derived from base units. E.g. Charge in coulombs This comes from :Charge = Current x time so… coulombs = amps x seconds or…C = A x s so…C could be written in base units as As (amp seconds)

Homogeneity If the units of both side of an equation can be proved to be the same, we say it is dimensionally homogeneous. E.g. Velocity = Frequency x wavelength ms -1 = s -1 x m ms -1 = ms -1 homogeneous, therefore this formula is correct.

Dimensional Analysis The dimensions of a physical quantity show how it is related to base quantities. Dimensional homogeneity and a bit of guesswork can be used to prove simple equations. E.g. Experimental work suggests that the period of oscillation of a pendulum moving through small angles depends upon its length, mass and the gravitational field strength, g.

So we can write Period = k m x l y g z Where k is a dimensionless constant and x,y and z are unknown numbers. So…s = kg x m y (ms -2 ) z s 1 = kg x m y+z s -2z Now equate both sides of the equation: For s1 = -2z so z = -1/2 For kg0 = x For m0 = y+z so y = +1/2 So… Period = k m 0 l 1/2 g -1/2 Or…Period = k l g

Q. Consider a sphere (radius, r) moving through a fluid of viscosity η at velocity v. Experimental work suggests that the force acting upon it is related to these quantities. Use dimensional analysis to determine the formula. (Note: the units of viscosity are Nsm -2 ) A.You should prove… F = k ηrv (F = 6π ηrv)

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