The mass defect of the nuclear reaction `._(5)B^(8) rarr ._(4)Be^(8) + ._(1)e^(0)` is `Delta m`, the wrong expression `"is"//"are"`

Options

A. `Delta m =` atomic mass of `(._(4)Be^(8) - ._(5)B^(8))`
B. `Delta m =` atomic mass of `(._(4)Be^(8) - ._(5)B^(8)) +` mass of one electron
C. `Delta m =` atomic mass of `(._(4)Be^(8) - ._(5)B^(8)) +` mass of one positron
D. `Delta m =` atomic mass of `(._(4)Be^(8) - ._(5)B^(8)) +` mass of two electrons

Answer

To solve the problem regarding the mass defect of the nuclear reaction \( _{5}^{8}B \rightarrow _{4}^{8}Be + _{1}^{0}e \), we will follow these steps:

### Step 1: Write the Nuclear Reaction
The nuclear reaction given is:
\[ _{5}^{8}B \rightarrow _{4}^{8}Be + _{1}^{0}e \]
This indicates that one boron-8 nucleus transforms into one beryllium-8 nucleus and one positron.

### Step 2: Identify the Masses
Next, we will identify the masses of the reactants and products involved in the reaction:
- Mass of Boron-8 (\( _{5}^{8}B \)) = \( m_B \)
- Mass of Beryllium-8 (\( _{4}^{8}Be \)) = \( m_{Be} \)
- Mass of Positron (\( _{1}^{0}e \)) = \( m_e \)

### Step 3: Calculate the Mass Defect
The mass defect (\( \Delta m \)) is defined as the difference between the mass of the reactants and the mass of the products. Thus, we can express it as:
\[ \Delta m = m_B - (m_{Be} + m_e) \]
This can be rearranged as:
\[ \Delta m = m_B - m_{Be} - m_e \]

### Step 4: Analyze the Expression
We can also express this in a different way:
\[ \Delta m = m_{Be} - m_B + m_e \]
However, the correct expression for the mass defect in terms of the initial mass minus the final mass is:
\[ \Delta m = m_B - (m_{Be} + m_e) \]

### Step 5: Identify the Wrong Expression
From the analysis, we can conclude that the correct expression for the mass defect is:
\[ \Delta m = m_B - (m_{Be} + m_e) \]
Any other formulation that does not follow this structure would be considered incorrect.

### Final Answer
The wrong expression regarding the mass defect in this nuclear reaction is any expression that does not conform to the above formula.

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