A nuclear reaction along with the masses of the particle taking part in it is as follows
`underset("amu")underset(1.002)A+underset("amu")underset(1.004)Btounderset("amu")underset(1.001)C+underset("amu")underset(1.003)D+QMeV`
The energy Q liberated in the reaction is

Options

A. `1.234MeV`
B. `0.931MeV`
C. `0.465MeV`
D. `1.862 MeV`

Explanation

To find the energy Q liberated in the nuclear reaction, we can follow these steps:

### Step 1: Write down the masses of the particles involved in the reaction.
The reaction is given as:
\[ A + B \rightarrow C + D + Q \]
Where the masses are:
- Mass of A = 1.002 amu
- Mass of B = 1.004 amu
- Mass of C = 1.001 amu
- Mass of D = 1.003 amu

### Step 2: Calculate the total mass of the reactants.
The total mass of the reactants (A + B) is calculated as:
\[ \text{Total mass of reactants} = \text{mass of A} + \text{mass of B} = 1.002 \, \text{amu} + 1.004 \, \text{amu} = 2.006 \, \text{amu} \]

### Step 3: Calculate the total mass of the products.
The total mass of the products (C + D) is calculated as:
\[ \text{Total mass of products} = \text{mass of C} + \text{mass of D} = 1.001 \, \text{amu} + 1.003 \, \text{amu} = 2.004 \, \text{amu} \]

### Step 4: Find the mass defect.
The mass defect (Δm) is the difference between the total mass of the reactants and the total mass of the products:
\[ \Delta m = \text{Total mass of reactants} - \text{Total mass of products} = 2.006 \, \text{amu} - 2.004 \, \text{amu} = 0.002 \, \text{amu} \]

### Step 5: Convert the mass defect to energy.
Using Einstein's equation \( E = \Delta m c^2 \) and knowing that 1 amu corresponds to 931.5 MeV, we can calculate the energy released (Q):
\[ Q = \Delta m \times 931.5 \, \text{MeV/amu} = 0.002 \, \text{amu} \times 931.5 \, \text{MeV/amu} = 1.863 \, \text{MeV} \]

### Final Answer:
The energy Q liberated in the reaction is approximately:
\[ Q \approx 1.863 \, \text{MeV} \]