A nuclear decay is expressed as ltbr. `._(6)C^(11) rarr ._(5)B^(11)+beta^(+)+X`
Then the unknown particle `X` is

Options

A. Neutron
B. Anti neutrino
C. Neutrino
D. Proton

Answer

To solve the problem of identifying the unknown particle \( X \) in the nuclear decay reaction:

\[ _{6}^{11}C \rightarrow _{5}^{11}B + \beta^{+} + X \]

we will follow these steps:

### Step 1: Understand the decay process
In this decay, a carbon-11 nucleus is transforming into a boron-11 nucleus while emitting a positron (\( \beta^{+} \)). A positron is the antimatter counterpart of an electron and has a positive charge.

### Step 2: Conservation of charge
We need to conserve charge in the reaction. The initial charge from carbon-11 is +6 (since carbon has an atomic number of 6).

- The charge of boron-11 is +5.
- The charge of the emitted positron (\( \beta^{+} \)) is +1.

Let \( Z \) be the charge of the unknown particle \( X \). According to the conservation of charge:

\[ 6 = 5 + 1 + Z \]

Solving for \( Z \):

\[ Z = 6 - 5 - 1 = 0 \]

### Step 3: Conservation of mass number
Next, we need to conserve the mass number. The mass number of carbon-11 is 11.

- The mass number of boron-11 is also 11.
- The mass number of the emitted positron is 0.

Let \( A \) be the mass number of the unknown particle \( X \). According to the conservation of mass number:

\[ 11 = 11 + 0 + A \]

Solving for \( A \):

\[ A = 11 - 11 - 0 = 0 \]

### Step 4: Identify the unknown particle
From the calculations, we find that the charge \( Z \) and mass number \( A \) of the unknown particle \( X \) are both 0. A particle with zero charge and zero mass number is a neutrino.

In the case of beta plus decay, the emitted particle is a neutrino. Thus, the unknown particle \( X \) is:

\[ X = \text{neutrino} \]

### Final Answer
The unknown particle \( X \) is a **neutrino**.

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