What does this three-number isotope notation mean? [duplicate]

Question

What does the superscript $3+$ mean? $$_{21}^{45}\mathrm{Sc}^{3+}$$

I understand that $45$ is the atomic mass number and $21$ is the number of protons. Is the $3+$ to indicate that it is a particular isotope, or does it have some other meaning?

Answer 1

The superscript '$3+$' denotes a normalised electric charge. Charges are quantised, that is they take on only certain discrete values.

• Neutrons do not have a net charge ($q = 0 $).
• Electrons and protons have the same absolute charge^[footnote]. They have opposite, arbitrary signs. By historical convention, protons are assigned positive charges.

Hence,

$$\text{electric charge} = \text{no. of protons} - \text{no. of electrons.}$$

For shorthand purposes, we usually normalise the electric charge by dividing the total electric charge of our agreed system with the elementary charge $e$.^[footnote] This provides us an opportunity to operate with integer values in chemistry; there are fractional charges for quarks which were discovered later but these particles cannot be observed separately by current understanding.

Note also that we write '$3+$' instead of '$+3$' since we are, again by convention, counting charges (that is $+ + + $), not denoting the mathematical normalised charge itself.

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As of 2011, this is verified up to essentially $1$ part in $10^{21}$. The absolute charge of an electron (or charge of a proton) is called the elementary charge $e$, and

$$e=1.6021766208(98) \cdot 10^{-19}\ \mathrm{C}$$

where the parentheses designate a standard uncertainty (assuming a normal distribution, $\approx 0.68$ probability, coverage factor $k =1$).

ref: Mohr, P. J.; Newell, D. B.; Taylor, B. N. 'CODATA Recommended Values of the Fundamental Physical Constants: 2014'. Reviews of Modern Physics, 2016, 88 (3). DOI: 10.1103/RevModPhys.88.035009, freely available on arXiv here, also archived link.

Disclaimer: originally, I claimed that proton–electron charge symmetry is verified up to $1$ part in $10^{26}$. This was wrong, and based on a naive approach. Again, see How accurately is it known that protons have the same charge as electrons? for a correction.