A nuclear transformation is denoted by `X(n,alpha) rarr. _(3)^(7)Li`. Which of the following is the nucleus of element `X`

Options

A. (a)`._(5)Be^(11)`
B. (b)`._(5)B^(10)`
C. (c)`._(5)B^9`
D. (d)`._(6)C^(12)`

Answer

To solve the nuclear transformation denoted by \( X(n, \alpha) \rightarrow _{3}^{7}\text{Li} \), we need to identify the nucleus of element \( X \).

### Step-by-Step Solution:

1. **Understand the Reaction**: The reaction indicates that a neutron (\( n \)) is bombarding a nucleus \( X \) and producing lithium-7 (\( _{3}^{7}\text{Li} \)) and an alpha particle (\( \alpha \)). The alpha particle is essentially a helium nucleus, which has an atomic number of 2 and an atomic mass of 4.

2. **Write Down the Conservation Laws**: In nuclear reactions, both atomic mass (A) and atomic number (Z) must be conserved.

3. **Set Up the Mass Equation**:
- On the left-hand side (LHS), the atomic mass is \( A + 1 \) (where \( A \) is the atomic mass of nucleus \( X \)).
- On the right-hand side (RHS), the atomic masses are \( 7 \) (from lithium) and \( 4 \) (from the alpha particle).
- Therefore, we can write the equation:
\[ A + 1 = 7 + 4 \]
\[ A + 1 = 11 \]
\[ A = 10 \]

4. **Set Up the Atomic Number Equation**:
- On the LHS, the atomic number is \( Z \) (the atomic number of nucleus \( X \)).
- On the RHS, the atomic numbers are \( 3 \) (from lithium) and \( 2 \) (from the alpha particle).
- Therefore, we can write the equation:
\[ Z + 0 = 3 + 2 \]
\[ Z = 5 \]

5. **Identify the Element**: From the values obtained, we have:
- Atomic mass \( A = 10 \)
- Atomic number \( Z = 5 \)

The element with atomic number 5 is boron (B).

6. **Conclusion**: The nucleus of element \( X \) is boron with atomic mass 10 and atomic number 5, which can be denoted as \( _{5}^{10}\text{B} \).

### Final Answer:
The nucleus of element \( X \) is \( _{5}^{10}\text{B} \) (Boron).

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