Copper has two isotopes, \({}^{63}\mathrm{Cu}\) and \({}^{65}\mathrm{Cu}\). The isotope \({}^{63}\mathrm{Cu}\) has a mass of 62.93 u and a relative abundance of 69 per cent. The average atomic mass of copper is 63.55 u. The mass of the \({}^{65}\mathrm{Cu}\) isotope is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(64.93\ \mathrm{u}\)
The average atomic mass is the weighted average of the isotope masses. Each mass is weighted by its relative abundance. The abundance of \( {}^{65}\mathrm{Cu} \) is \( 100-69=31 \) per cent. Let its mass be \( m \).
\( \begin{aligned} 63.55 &= \frac{69\times62.93+31\times m}{100} \\ 31\,m &= 6355-4342.17 \\ m &= \frac{2012.83}{31} \\ &= 64.93\ \mathrm{u} \end{aligned} \)
Therefore, the heavier isotope of copper has a mass of 64.93 u, close to its mass number 65.
NCERT (2026-27):
Atomic Masses and Composition of Nucleus – “… Thus, the average mass of a chlorine atom is obtained by the weighted average of the masses of the two isotopes, which works out to be”
\( \displaystyle =\frac{75.4\times34.98+24.6\times36.98}{100}=35.47\ \mathrm{u} \)