The half-life period for a zero order reaction is equal to

Options

A. `(0.693)/(k)`
B. `(2k)/([R]_(0))`
C. `(2.303)/(k)`
D. `([R]_(0))/(2k)` (where `[R]_(0)` is initial concentration of reactant and k is rate constant).

Explanation

To find the half-life period for a zero-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Zero-Order Reaction**:
A zero-order reaction is one where the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero-order reaction can be expressed as:
\[ R = -\frac{d[R]}{dt} = k \]
where \( R \) is the concentration of the reactant, \( k \) is the rate constant, and \( t \) is time.

2. **Write the Integrated Rate Equation**:
For a zero-order reaction, the integrated rate equation is:
\[ [R] = [R_0] - kt \]
where \([R_0]\) is the initial concentration of the reactant.

3. **Define Half-Life**:
The half-life (\( t_{1/2} \)) is the time required for the concentration of the reactant to decrease to half of its initial concentration. Therefore, at half-life:
\[ [R] = \frac{[R_0]}{2} \]

4. **Substitute into the Integrated Rate Equation**:
Substitute \([R] = \frac{[R_0]}{2}\) into the integrated rate equation:
\[ \frac{[R_0]}{2} = [R_0] - kt_{1/2} \]

5. **Rearrange the Equation**:
Rearranging the equation gives:
\[ kt_{1/2} = [R_0] - \frac{[R_0]}{2} \]
Simplifying the right side:
\[ kt_{1/2} = \frac{[R_0]}{2} \]

6. **Solve for Half-Life**:
Now, solve for \( t_{1/2} \):
\[ t_{1/2} = \frac{[R_0]}{2k} \]

### Final Result:
The half-life period for a zero-order reaction is given by:
\[ t_{1/2} = \frac{[R_0]}{2k} \]