Atomic Structure and Isotopes: Question 9

Worked solution

Part (a): Protons and neutrons in magnesium-26

The proton number of magnesium is $12$, so every magnesium atom has $12$ protons, regardless of isotope.

For magnesium-26, the nucleon (mass) number is $26$, so:

$\text{neutrons} = 26 - 12 = 14$

Part (b): Relative atomic mass from three isotopic abundances

The relative atomic mass is a weighted mean of the isotopes’ mass numbers, weighted by their percentage abundance:

$A_r = \frac{(\text{mass}_1 \times \text{abundance}_1) + (\text{mass}_2 \times \text{abundance}_2) + (\text{mass}_3 \times \text{abundance}_3)}{100}$

Substituting the values for magnesium:

$A_r = \frac{(24 \times 79.0) + (25 \times 10.0) + (26 \times 11.0)}{100} = \frac{1896 + 250 + 286}{100} = \frac{2432}{100} = 24.32$

Giving the answer to 3 significant figures:

$A_r = 24.3$

Part (c): Why the isotopes react identically

Magnesium-24 and magnesium-26 both have proton number $12$, so a neutral atom of each isotope has $12$ electrons, arranged in the same electronic configuration, $2,8,2$. The extra $2$ neutrons in magnesium-26’s nucleus add mass but do not change the number or arrangement of electrons.

Because chemical reactions (such as reacting with dilute hydrochloric acid) depend on the arrangement of electrons, particularly in the outer shell, and not on the number of neutrons, samples made from either isotope alone would react in exactly the same way. Even though the magnesium-26 sample would have a slightly greater mass overall.

Final answers

• (a) Protons $= 12$, neutrons $= 14$.
• (b) $A_r = \boxed{24.3}$ (3 s.f.).
• (c) Both isotopes have 12 electrons in identical electronic configuration, so they have identical chemical reactivity.