Smallest Thing lessons
How small can things get?
A 3D zoom from a water molecule into its oxygen atom, the nucleus and one proton, with the size at each level.
Everything around you is made of smaller pieces. Zoom into a drop of water and you find molecules, then atoms, then a tiny nucleus.
Each step down reveals something smaller inside. This course follows that zoom as far as anyone has measured.
You will learn how to write tiny sizes, how scientists see them, and where today's physics runs out.
Powers of ten
Tiny sizes need lots of zeros, so scientists count the zeros instead. Every time you divide by ten, the power of ten goes down by one.
The 1 steps one decimal place right each time the size is divided by ten, with the matching power of ten and something that size.
A negative power counts the decimal places up to and including the 1. So 0.001=10^{-3}, a thousandth.
Practice: Powers of ten
Write a tiny size as a power of ten, or a power of ten as a decimal.
Scientific notation
Most sizes are not exactly a power of ten. Scientific notation writes them as a number from 1 to 10, times a power of ten.
A water molecule: 0.00000000028\ \text{m}=2.8\times10^{-10}\ \text{m}
To get there, hop the decimal point right until one digit sits in front of it. Each hop takes one off the power.
The decimal point hops right one digit at a time while the power of ten drops by one per hop.
Practice: Scientific notation
Write a real size in scientific notation, the number and the power in separate boxes.
Milli, micro, nano
Prefixes give friendly names to powers of ten. A millimetre (mm) is 10^{-3} m, a micrometre (µm) is 10^{-6} m and a nanometre (nm) is 10^{-9} m.
Below those come the picometre, 10^{-12} m, and the femtometre, 10^{-15} m. Each prefix is a thousand times smaller than the one before.
One size steps down through the units from metres to femtometres, the number growing a thousand times at each step.
Practice: Match the sizes
Match each prefix to its power of ten, then each thing to its size.
Cells, bacteria and viruses
Your body is built from tens of trillions of cells. A typical cell is about 10 µm across, a hundredth of a millimetre.
Bacteria are about ten times smaller, around 1 µm. Viruses are smaller again, often about 100 nm.
Pairs drawn to scale, from the width of a hair to an atom, zooming into the smaller of each pair.
How many atoms fit across a cell?
Cells are made of molecules, and molecules are made of atoms. A small atom is about 0.1 nm, or 10^{-10} m, across.
To compare two sizes, divide the bigger by the smaller. With powers of ten, that means subtracting the powers.
\frac{10^{-5}}{10^{-10}}(a cell divided by an atom)=10^{-5-(\textcolor{#f871b9}{-10})}(subtract the powers)=10^{5}=100000(a hundred thousand atoms across one cell)
Practice: Order by size
Put five things in order of size, largest first.
Practice: How many fit across?
Work out how many of one thing fit across another by dividing powers of ten.
Seeing the very small
Your eyes can just make out things about 0.1 mm across, like the width of a hair. A light microscope shows details down to about 200 nm.
An electron microscope goes much further, down to single atoms. To look inside the nucleus, physicists use particle accelerators.
A size ladder from a millimetre to below a proton, showing how far down each tool can see.
Why light can't show an atom
Light is a wave, and visible light has a wavelength of 400 to 700 nm. A microscope can't show details much smaller than about half the wavelength it uses.
An atom is thousands of times smaller than that, so light blurs atoms together. Electrons have a wavelength over 100,000 times shorter, so they can pick atoms out.
Two points imaged with light or with electrons: the blur from each tool either keeps them apart or merges them into one.
Practice: Pick the tool
Sort things by whether a light microscope, an electron microscope or a particle accelerator is needed to see them.
Inside an atom
An atom has a tiny nucleus at its centre, made of protons and neutrons. Much lighter electrons move around it.
The number of protons decides the element. Oxygen has 8 protons, so a neutral oxygen atom also has 8 electrons.
A 3D tour of an oxygen atom: its nucleus, its two shells and its eight electrons.
An atom is mostly empty
In 1909, Hans Geiger and Ernest Marsden fired alpha particles at thin gold foil. Most went straight through, but a few bounced back.
In 1911, Ernest Rutherford explained why: each atom has a tiny, heavy nucleus. It is tens of thousands of times smaller across than the atom, yet holds over 99.9% of its mass.
A zoom into the centre of a hydrogen atom, through thin electron cloud, until the nucleus finally appears; then the atom scaled up to everyday sizes.
The rest of the atom is not quite nothing. A thin cloud of electrons fills it.
Practice: Picture the empty atom
Questions on how empty an atom is and where its mass sits.
Inside the nucleus
A nucleus is a tight ball of protons and neutrons. An oxygen nucleus is about 6 fm across, and a single proton about 1.7 fm.
Protons and neutrons are made of smaller particles called quarks. A proton has two up quarks and one down quark, held together by gluons.
A 3D tour of a proton: two up quarks, one down quark and the gluons between them, with their charges adding up to +1.
A neutron has one up quark and two down quarks. Their charges add up to +\frac{2}{3}-\frac{1}{3}-\frac{1}{3}=0.
Practice: What is it made of?
Drag words into the gaps to say what each level is made of, from a water molecule down to quarks.
Do quarks have a size?
No experiment has ever measured a size for a quark or an electron. If they have one, it is smaller than about 10^{-18} m, over a thousand times smaller than a proton.
So physics treats them as points with no size at all. A sharper experiment could still change that.
Raise the collision energy to shrink the smallest detail a collider can see, and watch the quarks inside a proton stay points.
The Planck length
The Planck length is about 1.6\times10^{-35} m. Near this size, gravity and quantum physics should both matter at once, and today's theories stop working.
It is not known to be the smallest possible length. It marks where physics needs a new theory, called quantum gravity, that nobody has found yet.
The whole ladder from a person to the Planck length, with the explored part and the unexplored gap below it.
Practice: True or false
True or false statements about point particles, measured sizes and the Planck length.
Practice: Place them on the ladder
Drag each thing onto the rung of the size ladder that matches its power of ten.