To find the fraction of the heavier isotope in a chlorine sample, let's go through the detailed steps.
1. Define Variables:
- Let [tex]\( p \)[/tex] be the fraction of the heavier isotope (with atomic weight 37).
- The fraction of the lighter isotope (with atomic weight 35) will then be [tex]\( 1 - p \)[/tex].
2. Set Up the Equation:
- The atomic weight of chlorine is a weighted average of the weights of its isotopes. This can be represented as:
[tex]\[
35.5 = (1 - p) \cdot 35 + p \cdot 37
\][/tex]
- Simplify this equation:
[tex]\[
35.5 = 35(1 - p) + 37p
\][/tex]
3. Distribute and Combine Like Terms:
- Distribute the 35:
[tex]\[
35.5 = 35 - 35p + 37p
\][/tex]
- Combine the terms containing [tex]\( p \)[/tex]:
[tex]\[
35.5 = 35 + 2p
\][/tex]
4. Isolate the Fraction [tex]\( p \)[/tex]:
- Subtract 35 from both sides:
[tex]\[
0.5 = 2p
\][/tex]
- Solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{0.5}{2}
\][/tex]
[tex]\[
p = 0.25
\][/tex]
5. Convert to Percentage:
- To express [tex]\( p \)[/tex] as a percentage:
[tex]\[
p \times 100 = 0.25 \times 100 = 25\%
\][/tex]
Thus, the fraction of the heavier isotope (with atomic weight 37) in the sample is 0.25, and as a percentage, it is 25%.
The correct answer is:
(3) 25
