SI Units and Prefixes

There are 7 SI Base units that make up all the other units we use in physics. For this course, we only need to learn about 6 of the 7 base units. The base unit for light intensity (the candela) does not need to be leant for the AQA course. 

SI Base units are important to physics as they are the same in all languages and hence are used universally. Other units not in this list may be different in different languages or different units may be used in different countries. The 6 base units are:

Quantity	Base Unit	Symbol
Length	Metre	m
Time	Second	s
Mass	Kilogram	kg
Temperature	Kelvin	K
Current	Ampere/Amps	A
Amount of a Substance	Mole	mol

A derived unit is comprised of a combination of the above SI Base units. There are many more derived units than SI base units and these are the units you will be familiar with such as Newtons \left(\text{N}\right), Joules \left(\text{J}\right), Hertz \left(\text{Hz}\right) and many more. 

Each unit you use in physics can be broken down into its SI base units either by using the definition of the unit or by the equation for the quantity that the unit describes. You will come across many of these in this course. 

A lot of the units we cover in A Level physics will involve the use of very large or very small numbers. By  using prefixes in front of units we can avoid having to write very large or small numbers out in full.  For example, we may be looking at a wavelength of light that is 0.000000656 \text{ m}. Instead of writing this out each time, we can use the prefix nano \left(\text{n}\right), and write out wavelength as 656 \text{ nm}. A full list of the prefixes you need to know can be found below: 

Prefix	Abbreviation	Number	Power of 10
Terra	T	1000000000000	1012
Giga	G	1000000000	109
Mega	M	1000000	106
Kilo	k	1000	103
Centi	c	0.01	10-2
Milli	m	0.001	10-3
Micro	u	0.000001	10-6
Nano	n	0.000000001	10-9
Femto	f	0.000000000001	10-12

Sometimes we are given numbers with units using the prefixes above. We cannot use these numbers into our calculations so we need to ensure we convert back to full numbers for our calculations. 

 

Example: Calculate the speed of a wave with wavelength 500 \text{ nm} and frequency 3.9 \text{ GHz}.

[3 marks]

To calculate this we need to convert \text{nm} and \text{GHz} back to \text{m} and \text{Hz}. We can use the table above for a guide. 

500\text{ nm} becomes 500 \times 10^{-9} \text{ m} and 3.9 \text{ GHz} becomes 3.9 \times 10^{9} \text{ Hz}.

Now we are ready to calculate using \text{velocity} = \text{wavelength} \times \text{frequency} (found on your data sheet). 

500 \times 10^{-9} \text{ m} \times 3.9 \times 10^9 \text{ Hz} = \bold{1950} \textbf{ms}\bold{^{-1}}

Across the physics course you will often need to convert between equivalent units. An equivalent unit is another unit given to the same quantity. For example energy could be measured in Joules or Calories. Here are a couple of useful conversions for you should know and be able to recall where needed:

Joules to electronvolts (\text{J to eV}):

• To convert from \text{J} to \text{eV} you need to divide by 1.6 \times 10^{-19}
• To convert from \text{eV} to \text{J} you need to multiply by 1.6 \times 10^{-19}

These conversions are particularly useful when dealing with very low quantities of energy. 

Joules to kilowatt-hours \text{(J to kWh)}

• To convert from \text{J} to \text{kWh} you need to divide by 3.6 \times 10^6  (amount of energy used by a 1\text{ kW} appliance in 1 \text{ hour}) 
• To convert from \text{kWh} to \text{J} you need to multiply by 3.6 \times 10^6  (amount of energy used by a 1\text{ kW} appliance in 1 \text{ hour}) 

These conversions allow you to work out how much energy has been used by an appliance over a period of time.