A radioactiv element has atomic number A and mass number M. It emits one `alpha` - particle .The atomic number and mass number of new element will be

Options

A. A-2,M-4
B. A-2,M
C. A,M-2
D. A-4,M-2

Answer

To solve the problem of determining the atomic number and mass number of a new element after a radioactive element emits an alpha particle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The atomic number (Z) is the number of protons in the nucleus of an atom.
- The mass number (A) is the total number of protons and neutrons in the nucleus.

2. **Identify the Initial Values**:
- Let the initial atomic number of the radioactive element be \( A \).
- Let the initial mass number of the radioactive element be \( M \).

3. **Know the Characteristics of an Alpha Particle**:
- An alpha particle is essentially a helium nucleus, which has:
- Atomic number = 2
- Mass number = 4

4. **Determine the Changes After Emission**:
- When an alpha particle is emitted, the atomic number of the original element decreases by 2 (because 2 protons are lost).
- The mass number of the original element decreases by 4 (because 4 nucleons are lost).

5. **Calculate the New Atomic Number and Mass Number**:
- New atomic number \( Z' = A - 2 \)
- New mass number \( M' = M - 4 \)

6. **Conclusion**:
- After the emission of one alpha particle, the new atomic number and mass number of the element will be:
- Atomic number: \( A - 2 \)
- Mass number: \( M - 4 \)

### Final Answer:
- The atomic number of the new element will be \( A - 2 \).
- The mass number of the new element will be \( M - 4 \).

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