The following approximate sizes give an idea of orders of magnitude.
wavelength u.v. 10-8diameter of an atom 10-10diameter of the nucleus 10-14range of strong nuclear force 10-15All of these lengths are in metres.The order of magnitude of a quantity is the power of ten closest to its value. For example, the height of a person (about 1.7 m) is of order 100 m, and the diameter of the Earth (about 1.3 × 107 m) is of order 107 m.Orders of magnitude are used to estimate and to compare quantities. Two quantities that differ by one order of magnitude differ by a factor of about 10.Worked example: how many times wider is an atom than a nucleus?10-10 m ÷ 10-14 m = 104 So an atom is about 10 000 times wider than its nucleus: four orders of magnitude. Most of an atom is empty space.Estimates are also a quick check on a calculated answer. If a calculation gives the mass of a car as 106 kg, it is wrong by about three orders of magnitude, because a typical car has a mass of about 103 kg.When estimating, round each value to one significant figure or to the nearest power of ten, and give the answer to one significant figure.
wavelength u.v. 10-8diameter of an atom 10-10diameter of the nucleus 10-14range of strong nuclear force 10-15All of these lengths are in metres.The order of magnitude of a quantity is the power of ten closest to its value. For example, the height of a person (about 1.7 m) is of order 100 m, and the diameter of the Earth (about 1.3 × 107 m) is of order 107 m.Orders of magnitude are used to estimate and to compare quantities. Two quantities that differ by one order of magnitude differ by a factor of about 10.Worked example: how many times wider is an atom than a nucleus?