Calculate mass defect in the following reaction: `H_1^2 + H_1^3 to He_2^4+n_0^1`
(Given: mass `H^(2) = 2.014 am u, H^3 = 3.016 `amu He= 4.004,n =1.008amu)

Options

A. 0.018 amu
B. 0.18 amu
C. 0.0018 amu
D. 1.8 amu

Answer

To calculate the mass defect in the given nuclear reaction, we will follow these steps:

### Step 1: Identify the reactants and products
The reaction is:
\[ H_2^1 + H_3^1 \rightarrow He_4^2 + n_1^0 \]

Here, the reactants are:
- \( H_2^1 \) (Deuterium)
- \( H_3^1 \) (Tritium)

And the products are:
- \( He_4^2 \) (Helium)
- \( n_1^0 \) (Neutron)

### Step 2: Write down the given masses
- Mass of \( H_2^1 \) = 2.014 amu
- Mass of \( H_3^1 \) = 3.016 amu
- Mass of \( He_4^2 \) = 4.004 amu
- Mass of \( n_1^0 \) = 1.008 amu

### Step 3: Calculate the total mass of the reactants
The total mass of the reactants is the sum of the masses of \( H_2^1 \) and \( H_3^1 \):
\[ \text{Total mass of reactants} = \text{mass of } H_2^1 + \text{mass of } H_3^1 \]
\[ = 2.014 \, \text{amu} + 3.016 \, \text{amu} = 5.030 \, \text{amu} \]

### Step 4: Calculate the total mass of the products
The total mass of the products is the sum of the masses of \( He_4^2 \) and \( n_1^0 \):
\[ \text{Total mass of products} = \text{mass of } He_4^2 + \text{mass of } n_1^0 \]
\[ = 4.004 \, \text{amu} + 1.008 \, \text{amu} = 5.012 \, \text{amu} \]

### Step 5: Calculate the mass defect
The mass defect (\( \Delta m \)) is the difference between the total mass of the reactants and the total mass of the products:
\[ \Delta m = \text{Total mass of reactants} - \text{Total mass of products} \]
\[ = 5.030 \, \text{amu} - 5.012 \, \text{amu} = 0.018 \, \text{amu} \]

### Conclusion
The mass defect for the reaction \( H_2^1 + H_3^1 \rightarrow He_4^2 + n_1^0 \) is:
\[ \Delta m = 0.018 \, \text{amu} \]

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