For the given series reaction in `n^(th)` step, find out the number of protons & energy.
`_(92)U^(238)rarr Ba+Kr+3_(0)n^(1)+"Energy" (E)`

Explanation

To solve the problem of finding the number of protons and energy in the given nuclear reaction step, we will follow these steps:

### Step 1: Understand the Reaction
The reaction given is:
\[ _{92}^{238}U \rightarrow Ba + Kr + 3_{0}^{1}n + \text{Energy} \]
This indicates that Uranium-238 undergoes fission to produce Barium, Krypton, and three neutrons, along with the release of energy.

### Step 2: Identify the Number of Protons
In nuclear reactions, the number of protons is conserved. Uranium-238 has 92 protons. The products of the reaction (Barium and Krypton) must also account for the protons from Uranium.

1. **Protons from Uranium**: 92 protons
2. **Protons from Barium (Ba)**: Barium has an atomic number of 56 (thus 56 protons).
3. **Protons from Krypton (Kr)**: Krypton has an atomic number of 36 (thus 36 protons).
4. **Total Protons in Products**:
\[ \text{Total Protons} = 56 + 36 = 92 \]
This confirms that the number of protons is conserved.

### Step 3: Determine the Number of Neutrons
In the reaction, we are given that 3 neutrons are produced. In a series of reactions, each neutron can potentially cause further fission reactions.

1. **Neutrons Produced**: 3 neutrons in the first step.
2. **Subsequent Reactions**: Each neutron can cause further fission, leading to more neutrons being produced. In the nth step, the number of neutrons can be expressed as:
\[ \text{Neutrons} = 3^n \]
This is because each neutron can lead to three more neutrons in subsequent reactions.

### Step 4: Calculate the Energy Released
The energy released in nuclear fission can also be expressed in terms of the number of reactions.

1. **Energy from Initial Reaction**: Let's denote the energy released in the first reaction as \( E \).
2. **Energy from Subsequent Reactions**: Each of the 3 neutrons can cause further reactions, each releasing energy \( E \). Thus, in the nth step:
\[ \text{Total Energy} = E + 3E + 9E + \ldots \]
The energy can be expressed as a geometric series. The total energy released in the nth step can be represented as:
\[ \text{Total Energy} = 3^n - 1 \cdot E \]
3. **Generic Formula for Energy**: The energy released in the nth reaction can be expressed as:
\[ \text{Energy} = (3^n - 1)E \]

### Final Answers
- **Number of Protons**: \( 3^n \)
- **Energy**: \( (3^n - 1)E \)