A radioactive nucleus can decay by three different processes. Half life for first process is 2 hours . Effective half life of the necleus is `4/3` hours. Find the half for second process in hours.

Explanation

To solve the problem, we need to find the half-life for the second decay process of a radioactive nucleus, given the half-life for the first process and the effective half-life of the nucleus.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Half-life for the first process, \( t_1 = 2 \) hours.
- Effective half-life of the nucleus, \( t = \frac{4}{3} \) hours.
- We need to find the half-life for the second process, \( t_2 \).

2. **Use the Effective Half-Life Formula:**
The effective half-life \( t \) can be expressed in terms of the half-lives of the individual processes:
\[ \frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2} \]

3. **Substitute the Known Values:**
Substitute \( t \) and \( t_1 \) into the equation:
\[ \frac{1}{\frac{4}{3}} = \frac{1}{2} + \frac{1}{t_2} \]

4. **Simplify the Left Side:**
The left side simplifies to:
\[ \frac{3}{4} = \frac{1}{2} + \frac{1}{t_2} \]

5. **Rearrange the Equation:**
To isolate \( \frac{1}{t_2} \), we can rearrange the equation:
\[ \frac{1}{t_2} = \frac{3}{4} - \frac{1}{2} \]

6. **Find a Common Denominator:**
The common denominator for \( \frac{3}{4} \) and \( \frac{1}{2} \) is 4:
\[ \frac{1}{t_2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \]

7. **Calculate \( t_2 \):**
Taking the reciprocal gives us:
\[ t_2 = 4 \text{ hours} \]

### Final Answer:
The half-life for the second process is **4 hours**.