Which of the following is not correct

Options

A. `t_(1//2)=(0.693)/(k)`
B. `N=N_(0)e^(-kt)`
C. `(1)/(N)-(1)/(N_(0))=1nkt_(1//2)`
D. None of these

Explanation

To solve the question "Which of the following is not correct?" regarding first-order reactions, we will analyze the statements provided in the options.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
- In a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant.

2. **Half-Life of First-Order Reactions**:
- The half-life (t₁/₂) of a first-order reaction is given by the formula:
\[ t_{1/2} = \frac{0.693}{k} \]
- Here, \( k \) is the rate constant. This statement is correct.

3. **Concentration Relation**:
- For a first-order reaction, the relationship between the concentration of reactants over time can be expressed as:
\[ n = n_0 e^{-kt} \]
- Where \( n \) is the concentration at time \( t \), and \( n_0 \) is the initial concentration. This statement is also correct.

4. **Logarithmic Form**:
- Taking the natural logarithm of both sides of the equation \( n = n_0 e^{-kt} \), we get:
\[ \ln(n) = \ln(n_0) - kt \]
- Rearranging gives:
\[ \ln\left(\frac{n}{n_0}\right) = -kt \]
- This is a valid transformation and is correct.

5. **Identifying the Incorrect Statement**:
- If we analyze the statements, it appears that the third option mentioned in the video transcript is incorrect. The video suggests that there is a misunderstanding or misrepresentation of the logarithmic relation, which is indeed correct when applied properly.

### Conclusion:
- The statement that is not correct would be the one that misrepresents the logarithmic relationship or any other statement that contradicts the established principles of first-order kinetics.