`""_(92) U^(238)` (IIIB) undergoes following emissions `:`
`""_(92)U^(238) overset( - alpha)(rarr) A overset( - alpha)(rarr) B overset( -beta)(rarr) C `
Which is `//` are correct statements

Options

A. A will be of IB group
B. A will be of IIIB group
C. B will be of IA group
D. C will be of IIIA group

Answer

To solve the problem, we will analyze the decay sequence of Uranium-238 (U-238) as it undergoes alpha and beta emissions step by step.

### Step 1: Identify the initial element
The initial element is Uranium-238, represented as:
\[ \text{U}_{92}^{238} \]
Here, the atomic number (Z) is 92 and the mass number (A) is 238.

### Step 2: First alpha emission
During the first alpha emission, a helium nucleus (which has an atomic number of 2 and a mass number of 4) is emitted. This results in:
- Atomic number decreases by 2: \( 92 - 2 = 90 \)
- Mass number decreases by 4: \( 238 - 4 = 234 \)

Thus, the new element (A) is:
\[ \text{A}_{90}^{234} \]
The element with atomic number 90 is Thorium (Th).

### Step 3: Second alpha emission
Now, element A (Thorium-234) undergoes another alpha emission:
- Atomic number decreases by 2: \( 90 - 2 = 88 \)
- Mass number decreases by 4: \( 234 - 4 = 230 \)

Thus, the new element (B) is:
\[ \text{B}_{88}^{230} \]
The element with atomic number 88 is Radium (Ra).

### Step 4: Beta emission
Next, element B (Radium-230) undergoes beta emission. In beta emission, a beta particle (which is an electron with a charge of -1) is emitted:
- Atomic number increases by 1: \( 88 + 1 = 89 \)
- Mass number remains the same: \( 230 \)

Thus, the new element (C) is:
\[ \text{C}_{89}^{230} \]
The element with atomic number 89 is Actinium (Ac).

### Step 5: Determine the groups of each element
Now, we need to determine the group of each element:
- Uranium (U) is in group 3B.
- Thorium (Th) is also in group 3B.
- Radium (Ra) is in group 2A.
- Actinium (Ac) is in group 3B.

### Conclusion
The correct statements based on the analysis are:
1. A (Thorium) is in group 3B.
2. B (Radium) is in group 2A.
3. C (Actinium) is in group 3B.

### Final Answer
The correct statement is:
- A will be of group 3B.
- B will be of group 2A.
- C will be of group 3B.