If the binding energy per nucleon of deuterium is 1.115 MeV, its mass defect in atomic mass unit is

Options

A. 0.0048
B. 0.0024
C. 0.0012
D. 0.0006

Explanation

To find the mass defect of deuterium given its binding energy per nucleon, we can follow these steps:

### Step 1: Understand the relationship between binding energy per nucleon and total binding energy
The binding energy per nucleon (E_bn) is given as 1.115 MeV. The total binding energy (E_b) can be calculated using the formula:
\[ E_b = E_{bn} \times A \]
where \( A \) is the number of nucleons in deuterium. Since deuterium has 2 nucleons (1 proton and 1 neutron), we have:
\[ E_b = 1.115 \, \text{MeV} \times 2 \]

### Step 2: Calculate the total binding energy
Now, substituting the values:
\[ E_b = 2 \times 1.115 \, \text{MeV} = 2.230 \, \text{MeV} \]

### Step 3: Relate binding energy to mass defect
The binding energy is also related to the mass defect (\( \Delta m \)) by the equation:
\[ E_b = \Delta m \cdot c^2 \]
where \( c \) is the speed of light. To find the mass defect in atomic mass units (u), we need to convert the binding energy from MeV to atomic mass units using the conversion factor:
\[ 1 \, \text{u} = 931.5 \, \text{MeV} \]

### Step 4: Calculate the mass defect
Rearranging the equation for mass defect gives:
\[ \Delta m = \frac{E_b}{c^2} \]
Substituting \( E_b \) in MeV and converting it to atomic mass units:
\[ \Delta m = \frac{2.230 \, \text{MeV}}{931.5 \, \text{MeV/u}} \]

### Step 5: Perform the calculation
Calculating the mass defect:
\[ \Delta m = \frac{2.230}{931.5} \approx 0.0024 \, \text{u} \]

### Conclusion
The mass defect of deuterium in atomic mass units is approximately:
\[ \Delta m \approx 0.0024 \, \text{u} \]