In `._88Ra^(226)` nucleus, there are.

Options

A. `138` protons and `88` neutrons
B. `138` neutrons and `88` protons
C. `226` protons and `88` electrons
D. `226` neutrons and `138` electrons

Explanation

To determine the number of protons and neutrons in the nucleus of the radium isotope \( ^{226}_{88}\text{Ra} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Values of A and Z**:
- In the notation \( ^{A}_{Z}\text{X} \), \( A \) is the mass number (total number of protons and neutrons) and \( Z \) is the atomic number (number of protons).
- For radium \( ^{226}_{88}\text{Ra} \):
- \( A = 226 \)
- \( Z = 88 \)

2. **Calculate the Number of Protons**:
- The number of protons in the nucleus is equal to the atomic number \( Z \).
- Therefore, the number of protons = \( Z = 88 \).

3. **Calculate the Number of Neutrons**:
- The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = A - Z \]
- Substituting the values:
\[ \text{Number of Neutrons} = 226 - 88 = 138 \]

4. **Summary of Results**:
- Number of Protons: \( 88 \)
- Number of Neutrons: \( 138 \)

### Final Answer:
- In the nucleus of \( ^{226}_{88}\text{Ra} \), there are **88 protons** and **138 neutrons**.