How to Get the Volume of an Atom's Nucleus
- 1). Select the element of interest and record the atomic number of the element. To find the volume of the nucleus, you must find the radius of the nucleus of the atom.
- 2). Use the equation derived from Rutherford's pioneering work with atoms and nuclei. The equation that defines the radius of the nucleus as the product of the equation R = R0 * A^1/3. A is the atomic number of the element of interest and R0 is a constant that ranges from 1.1 to 1.2 fermimeter (fm), depending on the case.
- 3). Calculate the radius of the nucleus by inserting the atomic number of the atom of interest into the equation and working out the answer. For example, assume that the element in question is number 8, carbon, and use the value of 1.1 fm (1 fm equals 1 x 10^-15 m). Keep all units in meters. Insert the atomic number into the equation and solve for R. R = R0A^1/3 = 1.1 x 10^-15 * 8^(1/3) = 1.1 x 10^-15 * 2 = 2.2 x 10^-15 m.
- 4). Draw on the geometric equation for volume of a sphere to calculate the volume of the nucleus. The equation for the volume of a sphere is V = 4/3 * pi * r^3, where r is the radius of the sphere. The nucleus of an atom is spherical in shape to minimize the energy required to hold the particles of the nucleus together.
- 5). Insert the value of the radius of the nucleus to obtain the volume of the nucleus of the atom. In the example, V = 4/3 * pi * r^3 = 4/3 * pi * (2.2 X 10^-15)^3 = 4.46 x 10^-44 m^3.
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