Typical size of atoms
Definition
Molecule
A particle made of two or more atoms chemically bonded together.
- Atoms and small molecules are extremely small, with a typical diameter of about 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m.
- Written out in full, 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m is 0.0000000001 m0.0000000001\ \text{m}0.0000000001 m, which is one ten-billionth of a metre.
- This value can also be written as 0.1 nm0.1\ \text{nm}0.1 nm, because one nanometre is 1×10−9 m1 \times 10^{-9}\ \text{m}1×10−9 m.
- Different atoms do have slightly different sizes, but almost all of them have diameters between about 0.5×10−10 m0.5 \times 10^{-10}\ \text{m}0.5×10−10 m and 5×10−10 m5 \times 10^{-10}\ \text{m}5×10−10 m, so they share the same order of magnitude.
- A small molecule, such as a water molecule made of three atoms, is only a few atoms across, so it has a size on the same scale of about 10−10 m10^{-10}\ \text{m}10−10 m.
- Large molecules, such as proteins or plastics, contain thousands of atoms and are much bigger, so the value 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m only applies to atoms and small molecules.
- Atoms are far smaller than the wavelength of visible light, so they cannot be seen with an ordinary light microscope.
Orders of magnitude
Definition
Order of magnitude
The power of ten closest to the size of a quantity.
Definition
Standard form
A way of writing a number as a value from 1 up to, but not including, 10 multiplied by a power of ten.
- Very large and very small quantities are compared using their order of magnitude, which is the power of ten closest to the quantity.
- The order of magnitude of an atom is 10−10 m10^{-10}\ \text{m}10−10 m.
- Numbers of this size are written in standard form, with a number from 111 up to, but not including, 101010 multiplied by a power of ten.
- A negative power of ten shows a number smaller than 111, and the more negative the power, the smaller the number.
- Two quantities differ by one order of magnitude when one is about 101010 times the other, and by two orders of magnitude when one is about 100100100 times the other.
- To find how many orders of magnitude separate two quantities, subtract the power of ten of the smaller one from the power of ten of the larger one.
Example
Converting a molecule size
- A small molecule has a measured width of 0.28 nm0.28\ \text{nm}0.28 nm.
- Using 1 nm=1×10−9 m1\ \text{nm} = 1 \times 10^{-9}\ \text{m}1 nm=1×10−9 m, the width is 0.28×10−9 m0.28 \times 10^{-9}\ \text{m}0.28×10−9 m.
- In standard form this becomes 2.8×10−10 m2.8 \times 10^{-10}\ \text{m}2.8×10−10 m.
- The nearest power of ten is 10−10 m10^{-10}\ \text{m}10−10 m, so the molecule has the typical order of magnitude of a small molecule.
Comparing sizes
- A human hair has a width of about 1×10−4 m1 \times 10^{-4}\ \text{m}1×10−4 m, which is six orders of magnitude larger than an atom.
- This means roughly one million atoms would fit side by side across the width of a single hair.
- A grain of fine sand is about 1×10−4 m1 \times 10^{-4}\ \text{m}1×10−4 m to 1×10−3 m1 \times 10^{-3}\ \text{m}1×10−3 m across, so even the smallest speck visible to the eye contains an enormous number of atoms.
- A nucleus, with a radius of around 10−14 m10^{-14}\ \text{m}10−14 m to 10−15 m10^{-15}\ \text{m}10−15 m, is four to five orders of magnitude smaller than the atom it sits in.
Example
Atoms across a millimetre
- A line 1 mm1\ \text{mm}1 mm long is drawn in pencil, which is 1×10−3 m1 \times 10^{-3}\ \text{m}1×10−3 m.
- Each atom has a typical diameter of 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m.
- Number of atoms along the line =1×10−31×10−10= \dfrac{1 \times 10^{-3}}{1 \times 10^{-10}}=1×10−101×10−3.
- Dividing powers of ten means subtracting the indices, so 10−3−(−10)=10710^{-3-(-10)} = 10^{7}10−3−(−10)=107.
- About 1×1071 \times 10^{7}1×107, or ten million, atoms would fit side by side along the line.
Exam technique
Recalling the size of an atom
- When asked for the typical size of an atom or small molecule, give 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m and always include the unit.
- In a multiple choice question, check the sign of the power, because 1×1010 m1 \times 10^{10}\ \text{m}1×1010 m is a huge distance, not a tiny one.
- When comparing sizes, divide the larger value by the smaller one and state the answer as a number of times or as a number of orders of magnitude.
- Show the division of powers of ten on the page, because the working can earn credit even if the final value is wrong.
Common Mistake
- Do not confuse the size of an atom, about 10−10 m10^{-10}\ \text{m}10−10 m, with the much smaller size of its nucleus.
- Do not write the power of ten as positive, because 101010^{10}1010 is ten billion, not one ten-billionth.
- Do not describe atoms as the size of dust or specks, because even the smallest visible particle contains billions of atoms.
Self review
- State the typical size of an atom in metres.
- Write 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m in nanometres.
- Explain what is meant by the order of magnitude of a length.
- Calculate how many orders of magnitude separate a hair of width 10−4 m10^{-4}\ \text{m}10−4 m from an atom.
- Explain why the value 10−10 m10^{-10}\ \text{m}10−10 m does not apply to large molecules such as proteins.
