IGCSE Chemistry 0620: Finding Isotopic Abundance Algebraically from Relative Atomic Mass

A metallurgist analyses a sample of pure copper wire and finds it contains only two naturally occurring isotopes, copper-63 and copper-65. The relative atomic mass of this copper sample is found to be $63.55$ . Copper has proton number 29.

(a) State the number of protons and the number of neutrons in one atom of copper-65. [2]

(b) Let the percentage abundance of copper-63 in the sample be $x$ . Write an expression, in terms of $x$ , for the percentage abundance of copper-65. [1]

(c) Using your expression from (b) and the relative atomic mass given above, calculate the percentage abundance of copper-63 and of copper-65 in this sample. [3]

(d) Copper-63 and copper-65 have different numbers of neutrons. Explain, in terms of subatomic particles, why they can be extracted and used together as a single element, copper. [2]

Part (a): Protons and neutrons in copper-65

The proton number of copper is $29$ , so every copper atom has $29$ protons, regardless of isotope.

For copper-65, the nucleon (mass) number is $65$ , so:

$\text{neutrons} = 65 - 29 = 36$

Part (b): Expressing the abundance of copper-65

Since the sample contains only these two isotopes, their percentage abundances must add up to $100\%$ . If copper-63 has abundance $x$ :

$\text{abundance of copper-65} = (100 - x)$

Part (c): Solving for the percentage abundances

The relative atomic mass is the weighted mean of the two mass numbers:

$A_r = \frac{(63 \times x) + (65 \times (100-x))}{100} = 63.55$

Multiply both sides by $100$ :

$63x + 65(100-x) = 6355$

Expand the brackets:

$63x + 6500 - 65x = 6355$

Collect like terms:

$-2x = 6355 - 6500 = -145$

Solve for $x$ :

$x = \frac{-145}{-2} = 72.5$

So copper-63 has abundance $72.5\%$ , and copper-65 has abundance $100 - 72.5 = 27.5\%$ .

Check: $\dfrac{(63 \times 72.5) + (65 \times 27.5)}{100} = \dfrac{4567.5 + 1787.5}{100} = \dfrac{6355}{100} = 63.55$ ✓

Part (d): Why the isotopes can be used together as one element

Copper-63 and copper-65 both have proton number $29$ , so a neutral atom of each isotope has $29$ electrons, arranged in the same electronic configuration. The extra $2$ neutrons in copper-65’s nucleus add mass but do not change the number or arrangement of electrons.

Since chemical properties are controlled by electron arrangement, not by the number of neutrons, both isotopes behave identically in chemical reactions. This means the metallurgist does not need to separate them, they can be used together as the single element copper.

Final answers

(a) Protons $= 29$ , neutrons $= 36$ .
(b) Abundance of copper-65 $= (100-x)$ .
(c) Copper-63 $= \boxed{72.5\%}$ ; copper-65 $= \boxed{27.5\%}$ .
(d) Both isotopes have 29 electrons in identical electronic configuration, so they have identical chemical properties.