Isotopes

Definition (learn this wording). Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

Because the proton number $Z$ is the same, isotopes are the same element (same position in the Periodic Table). Because the neutron number differs, the nucleon number $A$ — and therefore the mass — differs.

Worked — chlorine. Chlorine has two common isotopes:

Isotope	Protons	Neutrons	Electrons
$^{35}_{17}\text{Cl}$	17	$35-17 = 18$	17
$^{37}_{17}\text{Cl}$	17	$37-17 = 20$	17

Same protons (17) and same electrons (17); only the neutron count differs.

More examples.

• Hydrogen: $^{1}_{1}\text{H}$ (protium), $^{2}_{1}\text{H}$ (deuterium), $^{3}_{1}\text{H}$ (tritium).
• Carbon: $^{12}_{6}\text{C}$, $^{13}_{6}\text{C}$, $^{14}_{6}\text{C}$.

Chemical properties are governed by electrons — specifically the number and arrangement of the outer-shell electrons, which control bonding and reactions.

Isotopes of an element have:

• the same number of electrons, and
• the same electronic configuration.

Therefore they form the same bonds and undergo the same chemical reactions at essentially the same rate. For example, $^{35}\text{Cl}$ and $^{37}\text{Cl}$ both react with sodium to form NaCl in exactly the same way.

Exam phrasing. "Isotopes have the same number of electrons / the same electronic configuration, and chemical properties depend on electrons, so their chemical properties are identical."

Physical properties that depend on mass differ between isotopes. The syllabus limits this to mass and density.

• The isotope with more neutrons has a greater mass.
• The atomic size (volume) is essentially unchanged (neutrons add mass, not significant volume), so the heavier isotope has a greater density ($\rho = m/V$).

Worked reasoning. $^{37}\text{Cl}$ is heavier than $^{35}\text{Cl}$ but occupies the same volume, so a sample of $^{37}\text{Cl}$ is denser.

Cambridge note. Other mass-dependent effects (e.g. slightly different rates of diffusion or boiling points) exist, but for 9701 you should restrict your answer to mass and density unless the question states otherwise.

Because a natural sample is a mixture of isotopes, the relative atomic mass ($A_r$) is the weighted mean of the isotopic masses:

$A_r = \frac{\sum (\text{isotopic mass} \times \text{relative abundance})}{\sum \text{relative abundances}}$

Worked — chlorine. $^{35}\text{Cl}$ is $75\%$ abundant and $^{37}\text{Cl}$ is $25\%$: $A_r = \frac{(35 \times 75) + (37 \times 25)}{100} = \frac{2625 + 925}{100} = 35.5$

This is why chlorine's $A_r$ on the data sheet is $35.5$ — a value between the two isotope masses, closer to the more abundant one.

Link. The relative abundances come from a mass spectrum (covered in 22.2 Mass spectrometry). The same weighted-mean calculation appears in both topics.