Mass number of a nucleus X is A and atomic number is Z. Find mass number and atomic number of the new nucleus (say Y) after the emission of m-alpha particles and n-beta particles.

Explanation

To solve the problem, we need to determine the mass number and atomic number of the new nucleus (Y) after the emission of m alpha particles and n beta particles from a nucleus (X) with mass number A and atomic number Z.

### Step-by-Step Solution:

1. **Understanding Alpha Particle Emission:**
- When an alpha particle (which consists of 2 protons and 2 neutrons) is emitted from a nucleus, the mass number decreases by 4 and the atomic number decreases by 2.
- Therefore, for m alpha particles emitted, the changes can be expressed as:
- Change in mass number = \( -4m \)
- Change in atomic number = \( -2m \)

2. **Understanding Beta Particle Emission:**
- When a beta particle (which is an electron) is emitted, the mass number remains unchanged, but the atomic number increases by 1.
- Therefore, for n beta particles emitted, the changes can be expressed as:
- Change in mass number = \( 0 \)
- Change in atomic number = \( +n \)

3. **Calculating the New Mass Number (A_Y):**
- The new mass number \( A_Y \) of nucleus Y after the emissions can be calculated as:
\[ A_Y = A - 4m + 0 = A - 4m \]

4. **Calculating the New Atomic Number (Z_Y):**
- The new atomic number \( Z_Y \) of nucleus Y after the emissions can be calculated as:
\[ Z_Y = Z - 2m + n \]

5. **Final Expressions:**
- The mass number of nucleus Y is:
\[ A_Y = A - 4m \]
- The atomic number of nucleus Y is:
\[ Z_Y = Z - 2m + n \]

### Summary:
- After the emission of m alpha particles and n beta particles from nucleus X:
- The mass number of nucleus Y is \( A_Y = A - 4m \)
- The atomic number of nucleus Y is \( Z_Y = Z - 2m + n \)