Atomic number, mass number and isotopes

Two numbers for every atom

You met these numbers in Class 9 and 10. Here is a short review, and then we go further.

• The atomic number $Z$ is the number of protons in the nucleus. It decides which element the atom is.
• The mass number $A$ is the number of protons plus neutrons. We call protons and neutrons by one name, nucleons.
• The number of neutrons is $N = A - Z$.

We write a nucleus as ${}^{A}_{Z}\text{X}$. For sodium, ${}^{23}_{11}\text{Na}$ has $Z = 11$, so $11$ protons. It has $A = 23$, so $N = 23 - 11 = 12$ neutrons. A neutral atom of it has $11$ electrons.

For an ion, the electrons change but the nucleus does not. The ion $\text{Na}^+$ has $11$ protons, $12$ neutrons and $10$ electrons.

Same Z, different A: isotopes

Isotopes are atoms of the same element, with the same $Z$ and different $A$. Hydrogen has three of them.

Isotopes have the same number of electrons, so their chemical properties are the same. Their physical properties differ, because the masses differ. Heavy water, $\text{D}_2\text{O}$, has a density of $1.107\ \text{g mL}^{-1}$ and boils at $101.4\ ^\circ\text{C}$, while ordinary water has a density of $1.000\ \text{g mL}^{-1}$ and boils at $100\ ^\circ\text{C}$.

Same A, different Z: isobars

Isobars are atoms of different elements with the same mass number. ${}^{40}_{18}\text{Ar}$ and ${}^{40}_{20}\text{Ca}$ are isobars, and so are ${}^{14}_{6}\text{C}$ and ${}^{14}_{7}\text{N}$.

Same N: isotones

Isotones are atoms of different elements with the same number of neutrons. ${}^{13}_{6}\text{C}$ has $N = 7$, and ${}^{14}_{7}\text{N}$ has $N = 7$. They are isotones. So are ${}^{39}_{19}\text{K}$ and ${}^{40}_{20}\text{Ca}$, with $N = 20$ each.

How do we find the isotopes? The mass spectrometer

A mass spectrometer weighs atoms, one kind at a time. It has four steps.

1. Ionise. A beam of fast electrons knocks an electron out of each atom, so the atoms become positive ions, $\text{X}^+$.
2. Accelerate. An electric field speeds up the ions. Each ion gets the same kinetic energy, $qV$.
3. Bend. The ions enter a magnetic field, which bends them into a circle of radius $r$. The force $qvB$ provides the centripetal force, so $r = \dfrac{mv}{qB}$. Using $qV = \tfrac{1}{2}mv^2$, we can show that $r = \dfrac{1}{B}\sqrt{\dfrac{2mV}{q}}$. For the same charge and the same voltage, a heavier ion moves in a bigger circle.
4. Detect. The ions land on a plate. The position tells us the mass, and the size of the signal tells us how many ions of that mass there are.

The result is a mass spectrum: a bar for each isotope, with a height that shows how common it is. Chlorine gives two bars, at mass numbers $35$ and $37$, with heights in the ratio $3 : 1$.

Average atomic mass

The atomic mass that you find in the periodic table is the weighted average of the masses of the isotopes of the element in a natural sample.

Magnesium has three isotopes: $78.99\ \%$ of ${}^{24}\text{Mg}$, $10.00\ \%$ of ${}^{25}\text{Mg}$ and $11.01\ \%$ of ${}^{26}\text{Mg}$. Using the mass numbers,

The table gives $24.305\ \text{u}$. The small difference is because a real isotope has a mass that is very close to its mass number, but not exactly equal. For example, the real mass of ${}^{24}\text{Mg}$ is $23.985\ \text{u}$. Using the exact masses gives $24.305\ \text{u}$.

Some elements have only one natural isotope, for example fluorine-19, sodium-23, aluminium-27 and phosphorus-31. Their atomic mass is almost a whole number.

You should find that the average sits nearer the taller bar, and halfway between only when both isotopes are equally common.

Practise with new numbers

Try it in Python

This program finds the average atomic mass of magnesium.

Remember these

• $Z$ is the number of protons, $A = Z + N$, and a neutral atom has $Z$ electrons.
• Isotopes: same $Z$. Isobars: same $A$. Isotones: same $N$.
• Isotopes have the same chemistry and different physical properties.
• In a mass spectrometer, the radius of the path is $r = \dfrac{1}{B}\sqrt{\dfrac{2mV}{q}}$. Heavier ions move in bigger circles.
• The atomic mass is the weighted average of the masses of the isotopes.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many protons, neutrons and electrons are there in the ion ${}^{35}_{17}\text{Cl}^-$?

2. Are ${}^{40}_{18}\text{Ar}$ and ${}^{40}_{19}\text{K}$ isotopes, isobars or isotones?

3. In a mass spectrometer, which ion follows the larger circle, ${}^{6}\text{Li}^+$ or ${}^{7}\text{Li}^+$?

4. Neon is $90.5\ \%$ neon-20, $0.3\ \%$ neon-21 and $9.2\ \%$ neon-22. Taking masses as mass numbers, what is its average atomic mass?