When a `beta`-particle is emitted by an atom of a radioactive element, the daughter nuclide formed possesses:

Options

A. same mass number but atomic number less by one unit
B. same mass number but atomic number less by two units
C. same mass number but atomic number higher by one unit
D. same mass number but atomic number higher by two units

Answer

To solve the question regarding the emission of a beta particle by a radioactive element and the characteristics of the daughter nuclide formed, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Beta Decay**:
- In beta decay, a neutron in the nucleus of a radioactive atom is transformed into a proton and an electron (the beta particle). The beta particle is then emitted from the nucleus.

2. **Identifying Initial Parameters**:
- Let’s denote the radioactive parent nuclide as having a mass number \( A \) and an atomic number \( Z \). Therefore, we can represent it as \( \text{Parent} \, ^A_Z \text{X} \).

3. **Transformation During Beta Decay**:
- When a beta particle is emitted, one neutron is converted into one proton. This means:
- The number of protons increases by 1 (from \( Z \) to \( Z + 1 \)).
- The number of neutrons decreases by 1 (from \( N \) to \( N - 1 \)).
- The mass number \( A \), which is the total number of protons and neutrons, remains unchanged because the total count of nucleons (protons + neutrons) does not change.

4. **Resulting Daughter Nuclide**:
- The daughter nuclide can be represented as \( \text{Daughter} \, ^A_{Z+1} \text{Y} \).
- Here, the mass number \( A \) remains the same, while the atomic number increases by 1.

5. **Conclusion**:
- Therefore, the daughter nuclide formed after the emission of a beta particle will have the same mass number \( A \) but an atomic number \( Z + 1 \).

### Final Answer:
The daughter nuclide formed possesses the same mass number but an atomic number that is higher by one unit.