how much energy is required to remove a neuton `(m_(n)=1.008 665u)` from `""_(7)^(15)N` that has an atomic mass of 15.000 108 to make `""_(7)^(14)N` that has an atomicmass of 14.003 074u?

Options

A. 1.163MeV
B. 939.6MeV
C. 6.423MeV
D. 928.7MeV

Answer

To find the energy required to remove a neutron from nitrogen-15 (N-15) to form nitrogen-14 (N-14), we can follow these steps:

### Step 1: Identify the masses involved
- Mass of neutron (m_n) = 1.008665 u
- Mass of nitrogen-15 (N-15) = 15.000108 u
- Mass of nitrogen-14 (N-14) = 14.003074 u

### Step 2: Write the nuclear reaction
The reaction can be represented as:
\[ {}_{7}^{15}\text{N} \rightarrow {}_{7}^{14}\text{N} + n \]
where \( n \) is the neutron being removed.

### Step 3: Calculate the mass defect (Δm)
The mass defect is calculated as the difference between the mass of the reactants and the mass of the products.

- Mass of reactants = Mass of N-15 = 15.000108 u
- Mass of products = Mass of N-14 + Mass of neutron = 14.003074 u + 1.008665 u

Calculating the mass of the products:
\[ \text{Mass of products} = 14.003074 + 1.008665 = 15.011739 \, \text{u} \]

Now, calculate the mass defect:
\[ \Delta m = \text{Mass of reactants} - \text{Mass of products} \]
\[ \Delta m = 15.000108 \, \text{u} - 15.011739 \, \text{u} \]
\[ \Delta m = -0.011631 \, \text{u} \]

### Step 4: Convert mass defect to energy
Using the conversion factor \( 1 \, \text{u} = 931.5 \, \text{MeV} \):
\[ \text{Energy} = \Delta m \times 931.5 \, \text{MeV} \]
\[ \text{Energy} = -0.011631 \, \text{u} \times 931.5 \, \text{MeV/u} \]
\[ \text{Energy} = -10.83 \, \text{MeV} \]

Since we are looking for the energy required to remove the neutron, we take the absolute value:
\[ \text{Energy required} = 10.83 \, \text{MeV} \]

### Final Answer:
The energy required to remove a neutron from nitrogen-15 to form nitrogen-14 is approximately **10.83 MeV**.

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