In the nuclear transmutation
`._(4)Be^(9)+X rarr ._(4)Be^(8)+Y`
`(X,Y)` is `//`are

Options

A. `(gamma,n)`
B. `(p,D)`
C. `(n,D)`
D. `(gamma,p)`

Explanation

To solve the nuclear transmutation equation given:

\[ \ _{4}^{9}\text{Be} + X \rightarrow \ _{4}^{8}\text{Be} + Y \]

we need to identify the particles \(X\) and \(Y\).

### Step 1: Analyze the Reaction
The reaction involves a beryllium-9 nucleus (\(_{4}^{9}\text{Be}\)) being transformed into a beryllium-8 nucleus (\(_{4}^{8}\text{Be}\)). This indicates that a particle \(X\) is bombarding the beryllium nucleus, resulting in the emission of another particle \(Y\).

### Step 2: Conservation of Atomic and Mass Numbers
In nuclear reactions, both the atomic number and mass number must be conserved.

- The atomic number of beryllium is 4, which remains the same on both sides of the equation.
- The mass number on the left side is 9 (from \(_{4}^{9}\text{Be}\)) and on the right side, we have 8 (from \(_{4}^{8}\text{Be}\)) plus the mass number of \(Y\).

### Step 3: Set Up the Equation
Since the mass number must be conserved, we can set up the following equation for the mass numbers:

\[ 9 = 8 + \text{mass number of } Y \]

From this, we can deduce that:

\[ \text{mass number of } Y = 9 - 8 = 1 \]

### Step 4: Identify Particle \(Y\)
Given that the mass number of \(Y\) is 1 and it is a neutral particle, \(Y\) must be a neutron (\(n\)), which has a mass number of 1 and an atomic number of 0.

### Step 5: Identify Particle \(X\)
Now we need to identify \(X\). Since the atomic number remains the same (4), and we know that a neutron is produced, the particle \(X\) must be a gamma particle (\(\gamma\)) which does not affect the atomic number or mass number.

### Conclusion
Thus, we can conclude that:

\[ X = \gamma \quad \text{(gamma particle)} \]
\[ Y = n \quad \text{(neutron)} \]

### Final Answer
So, the values of \(X\) and \(Y\) are:
- \(X\) is a gamma particle (\(\gamma\))
- \(Y\) is a neutron (\(n\))