# How can the atomic mass of an individual element be calculated given only the atomic number?

mathsworkmusic | (Level 2) Educator

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The atomic mass number `m_a `, atomic number `Z ` (number of protons in the atom, by which the periodic table is ordered - also equal to the number of electrons in the atom) and neutron number `N ` (number of neutrons in the atom) are related by the equation

`m_a = Z + N `

so that the atomic mass number `m_a ` is equal to the number of nucleons in the atom, that is the number of protons plus neutrons in the nucleus.

If we are only given/only know the atomic number `Z ` and not the neutron number `N ` we can approximately calculate the atomic mass number `m_a ` from `Z ` . This can be modelled as a piecewise linear relationship,

`m_a = 2Z `   for smaller `Z` (Helium, proton number = 2. NB Hydrogen has no neutrons, so has atomic mass = 1)

` = ((2 +2.5)/2) Z `  for medium `Z ` (Lithium (3) to Tin (50))

` = 2.5Z `   for larger `Z ` (Tin (50) to Ununoctium (118))

but a better fit (see link attached below) may be a power-law function given by

`m_a = 1.61Z^1.1 `

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See periodic table for atomic number and atomic mass number

www.ptable.com

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