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Atomic sizes and standard form

Atoms are so small that it is easier to write their size using standard form.

For example:

An atom of gold has a diameter of 0.000,000,000,144 m. To write this number in standard form:

• start with a decimal number equal to or more than 1, and less than 10
• in this case it's 1.44
• then, to work out the power of 10 count how many places the decimal point moves to make 1.44
• in this case it moves 10 times, so in standard form the diameter of a gold atom is 1.44 × 10^-10 m

Make sure you know how to input power of 10 on your calculator.

Order of magnitude estimation for the size of atoms and small molecules

Here are some typical atomic diameters:

The diameters are slightly different, but are all about 10^-10 m. The size of these atoms is said to have an order of magnitude of 10^-10.

To find the order of magnitude estimate, always round to the nearest power of 10.

Example - atom

An atom of oxygen has a diameter of 7.4 x 10^-11 m. Give an order of magnitude estimate of the size of an oxygen atom.

7.4 rounds up to 10

10 × 10^-11

= 1.0 × 10^-10 m

The order of magnitude estimate for an oxygen atom is 10^-10.

Example - molecule

A dodecane molecule contains a chain of 12 carbon atoms. Each atom has an order of magnitude of 10^-10. Give an order of magnitude estimate for the length of a molecule of dodecane.

12 × 10^-10

= 1.2 × 10^-9 m

The order of magnitude estimate for the size of a molecule of dodecane is 10^-9.