Question

What is average atomic mass of chlorine if its two isotopes \(\text{Cl}^{35}\) and \(\text{Cl}^{37}\) exists in relative abundance of \(75\%\) and \(25\%\) respectively ?

• A. \(35.0\)
• B. \(35.5\)
• C. \(37.0\)
• D. \(37.5\)

Hint:

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

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The atomic mass listed in the periodic table is not the mass of one isotope. It is the weighted average of all natural isotopes, where each isotope counts in proportion to its relative abundance.
Chlorine has two isotopes here, \(\text{Cl}^{35}\) at \(75\%\) and \(\text{Cl}^{37}\) at \(25\%\).

Step 2: Key Formula or Approach:
\[ \text{Average mass} = \frac{(m_1 \times a_1) + (m_2 \times a_2)}{100} \]
where \(m\) is the isotopic mass and \(a\) is the percentage abundance.

Step 3: Detailed Explanation:
Substitute the given values:
\[ \text{Average mass} = \frac{(35 \times 75) + (37 \times 25)}{100} = \frac{2625 + 925}{100} = \frac{3550}{100} = 35.5 \]
The answer must lie between 35 and 37 and sit closer to 35 because the lighter isotope is three times as abundant. This matches \(35.5\).

Step 4: Why the other options are wrong.
Option (A) \(35.0\) ignores the heavier isotope completely. Option (C) \(37.0\) ignores the lighter isotope. Option (D) \(37.5\) lies above both isotopic masses, which is impossible for a weighted average.

Final Answer:
The average atomic mass of chlorine is \(35.5\) u, option (B). \[ \boxed{35.5} \]