In a `alpha` -decay, the sequence is given as
`X overset(alpha)to X_(1) overset(beta)to X_(2)overset(alpha)to X_(3)`. The mass number and atomic number of X are 170 and 62 respectively. Calculate the same values for `X_(3)`.

Answer

To solve the problem, we need to analyze the decay sequence step by step. We start with the nucleus \( X \) which has a mass number (A) of 170 and an atomic number (Z) of 62.

1. **First Decay (Alpha Decay)**:
- In alpha decay, the nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This means:
- The mass number decreases by 4 (A - 4).
- The atomic number decreases by 2 (Z - 2).
- For nucleus \( X \):
- New mass number \( A_1 = 170 - 4 = 166 \)
- New atomic number \( Z_1 = 62 - 2 = 60 \)
- Thus, after the first decay, we have nucleus \( X_1 \) with \( A_1 = 166 \) and \( Z_1 = 60 \).

2. **Second Decay (Beta Decay)**:
- In beta decay, a neutron is transformed into a proton, which means:
- The mass number remains the same (A).
- The atomic number increases by 1 (Z + 1).
- For nucleus \( X_1 \):
- New mass number \( A_2 = 166 \) (remains the same)
- New atomic number \( Z_2 = 60 + 1 = 61 \)
- Thus, after the beta decay, we have nucleus \( X_2 \) with \( A_2 = 166 \) and \( Z_2 = 61 \).

3. **Third Decay (Alpha Decay)**:
- Again, we have another alpha decay from nucleus \( X_2 \):
- The mass number decreases by 4 (A - 4).
- The atomic number decreases by 2 (Z - 2).
- For nucleus \( X_2 \):
- New mass number \( A_3 = 166 - 4 = 162 \)
- New atomic number \( Z_3 = 61 - 2 = 59 \)
- Thus, after the second alpha decay, we have nucleus \( X_3 \) with \( A_3 = 162 \) and \( Z_3 = 59 \).

Finally, we summarize the values for nucleus \( X_3 \):
- Mass number \( A_3 = 162 \)
- Atomic number \( Z_3 = 59 \)

### Final Answer:
- Mass number of \( X_3 \): 162
- Atomic number of \( X_3 \): 59