Question

Chlorine has two isotopes \(\text{Cl}^{37}\) and \(\text{Cl}^{35}\) with percentage abundance of \(25\%\) and \(75\%\) respectively. Find average atomic mass of chlorine ?

• A. \(35\)
• B. \(37\)
• C. \(35.5\)
• D. \(36\)

Hint:

Average atomic mass is the abundance-weighted mean of the isotopic masses.

Answer 1

The Correct Option is C

Step 1: Idea
Treat the abundances as fractions of the atoms: 0.25 of the atoms are Cl-37 and 0.75 are Cl-35.

Step 2: Quick shortcut
Start from the lighter isotope, 35. The heavier isotope is 2 units heavier and makes up 25% of the atoms, so the average rises by $2 \times 0.25 = 0.5$.

Step 3: Result
\[ 35 + 0.5 = 35.5 \]
Cross-check with the direct sum: $0.25 \times 37 + 0.75 \times 35 = 9.25 + 26.25 = 35.5$.

Step 4: Why not the others
A plain mean of 35 and 37 gives 36, which wrongly treats both isotopes as equally common. The values 35 and 37 are single isotope masses. The weighted figure must be nearer 35, so 35.5 is the only sensible choice.

Final Answer:
The weighted average is 35.5 u. This is option (C). \[ \boxed{\text{(C) }35.5} \]