If the binding energy of the deuterium is `2.23 MeV`. The mass defect given in a.m.u. is.

Options

A. `-0.0024`
B. `-0.0012`
C. `0.0012`
D. `0.0024`

Explanation

To find the mass defect in atomic mass units (a.m.u.) given the binding energy of deuterium, we can use the relationship between binding energy and mass defect. The binding energy is given as 2.23 MeV, and we know that 1 a.m.u. corresponds to a binding energy of approximately 931 MeV.

### Step-by-Step Solution:

1. **Understand the relationship**: The mass defect (Δm) can be calculated using the formula:
\[ \Delta m = \frac{E}{c^2} \]
However, in this case, we will use the relationship between binding energy and mass defect directly.

2. **Use the conversion factor**: We know that:
\[ 1 \text{ a.m.u.} \approx 931 \text{ MeV} \]
This means that for every 931 MeV of binding energy, there is a mass defect of 1 a.m.u.

3. **Set up the proportion**: We need to find the mass defect corresponding to a binding energy of 2.23 MeV. We can set up the proportion:
\[ \frac{1 \text{ a.m.u.}}{931 \text{ MeV}} = \frac{\Delta m}{2.23 \text{ MeV}} \]

4. **Cross-multiply to solve for Δm**:
\[ \Delta m = \frac{2.23 \text{ MeV}}{931 \text{ MeV}} \times 1 \text{ a.m.u.} \]

5. **Calculate the mass defect**:
\[ \Delta m = \frac{2.23}{931} \text{ a.m.u.} \]
\[ \Delta m \approx 0.0024 \text{ a.m.u.} \]

### Final Answer:
The mass defect of deuterium is approximately **0.0024 a.m.u.**.