12 femtometri!
A uranium nucleus is the center of a uranium atom. It holds 92 protons and, in uranium-238, the most common kind, 146 neutrons. It is about 12 femtometers across, measured as twice its charge radius, the average radius of its electric charge. A femtometer is a millionth of a billionth of a meter (10−15 meters).
A nucleus has no hard edge, so its size is given as a charge radius. For uranium-238, a table of nuclear radii kept by the International Atomic Energy Agency (IAEA) gives 5.857 femtometers, known to better than 0.1%. That makes the nucleus 11.7 femtometers across. Uranium-235, which has three fewer neutrons, is very slightly smaller, 11.67 femtometers across.
A uranium nucleus has far more neutrons than protons. Protons push one another apart with their electric charge, while all the protons and neutrons pull on their nearest neighbors through the strong nuclear force. In a heavy nucleus, the extra neutrons are needed to keep the electric push from breaking it apart.
Uranium-238 is radioactive, but it decays extremely slowly. Its half-life, the time it takes half of a sample to decay, is 4.47 billion years. Earth is about 4.54 billion years old, so about half of the uranium-238 that Earth formed with is still here.
Uranium-238 decays by throwing out an alpha particle, which is a helium nucleus. A chain of further decays follows, ending in lead-206. Geologists use this chain, and a similar one that starts from uranium-235, to measure the ages of rocks and of Earth itself.
Uranium-235 makes up about 0.72% of natural uranium. Its nuclei split apart easily when struck by a neutron. Each split releases energy and more neutrons, which can go on to split other nuclei in a chain reaction. Nuclear power plants in the United States control this reaction to make heat for electricity, using fuel enriched to 3–5% uranium-235.