If the atomic number and the mass number of X are 72 and 180 then the mass number and atomic number of X4 are-

Options

A. 0.375 gm
B. 0.6 gm
C. 0.9 gm
D. 1 gm

Answer

To solve the problem, we need to determine the atomic number and mass number of the element X4 after it undergoes a series of decays. The given atomic number (Z) and mass number (A) of element X are 72 and 180, respectively.

### Step-by-Step Solution:

1. **Identify the Initial Values:**
- Atomic number (Z) of X = 72
- Mass number (A) of X = 180

2. **First Decay (Alpha Decay):**
- In alpha decay, the atomic mass decreases by 4 and the atomic number decreases by 2.
- New mass number (A1) = A - 4 = 180 - 4 = 176
- New atomic number (Z1) = Z - 2 = 72 - 2 = 70

3. **Second Decay (Beta Decay):**
- In beta decay, the atomic mass remains the same, but the atomic number increases by 1.
- New mass number (A2) = A1 = 176
- New atomic number (Z2) = Z1 + 1 = 70 + 1 = 71

4. **Third Decay (Alpha Decay):**
- Again, in alpha decay, the atomic mass decreases by 4 and the atomic number decreases by 2.
- New mass number (A3) = A2 - 4 = 176 - 4 = 172
- New atomic number (Z3) = Z2 - 2 = 71 - 2 = 69

5. **Fourth Decay (Alpha Decay):**
- For the final decay, we apply alpha decay once more.
- New mass number (A4) = A3 - 4 = 172 - 4 = 168
- New atomic number (Z4) = Z3 - 2 = 69 - 2 = 67

6. **Final Values:**
- The atomic number of X4 = 67
- The mass number of X4 = 168

### Conclusion:
The atomic number and mass number of X4 are:
- Atomic number (Z) = 67
- Mass number (A) = 168