Question

For n^th order of reaction, Half-life period is directly proportional to

• A. \(a^n-1\)
• B. \(a^{1-n}\)
• C. \(\frac{1}{a^{n-1}}\)
• D. \(\frac{1}{a^{1-n}}\)

Answer 1

The Correct Option is C

For an n^th order reaction (n ≠ 1), the half-life period (t_1/2) is given by the formula:

\( t_{1/2} \propto \frac{1}{a^{n-1}} \)

where:
- \( a \) is the initial concentration
- \( n \) is the order of the reaction

Correct Answer: \( \frac{1}{a^{n-1}} \)

Answer 2

For an n^th order reaction (where \( n \ne 1 \)), the expression for half-life is: 

$$ t_{1/2} \propto \frac{1}{a^{n - 1}} $$

Here, \( a \) is the initial concentration. Therefore, the half-life is inversely proportional to \( a^{n - 1} \).

Correct answer: \( \frac{1}{a^{n - 1}} \)