Assume that a neutron breaks into a proton and an electron . The energy reased during this process is (mass of neutron `= 1.6725 xx 10^(-27) kg` mass of proton `= 1.6725 xx 10^(-27) kg` mass of electron `= 9 xx 10^(-31) kg )`

Options

A. 0.73 MeV
B. 7.10 MeV
C. 6.30 MeV
D. 5.4 MeV

Answer

To find the energy released during the process of a neutron breaking into a proton and an electron, we can follow these steps:

### Step 1: Identify the masses involved
- Mass of neutron (m_n) = \(1.6725 \times 10^{-27} \, \text{kg}\)
- Mass of proton (m_p) = \(1.6725 \times 10^{-27} \, \text{kg}\)
- Mass of electron (m_e) = \(9 \times 10^{-31} \, \text{kg}\)

### Step 2: Calculate the change in mass (Δm)
The change in mass when a neutron breaks into a proton and an electron can be calculated using the formula:
\[ \Delta m = m_p + m_e - m_n \]
Substituting the values:
\[ \Delta m = (1.6725 \times 10^{-27} \, \text{kg}) + (9 \times 10^{-31} \, \text{kg}) - (1.6725 \times 10^{-27} \, \text{kg}) \]
\[ \Delta m = 9 \times 10^{-31} \, \text{kg} \]

### Step 3: Calculate the energy released (E)
Using Einstein's mass-energy equivalence principle, the energy released can be calculated using the formula:
\[ E = \Delta m \cdot c^2 \]
where \(c\) (the speed of light) is approximately \(3 \times 10^8 \, \text{m/s}\). Thus:
\[ E = (9 \times 10^{-31} \, \text{kg}) \cdot (3 \times 10^8 \, \text{m/s})^2 \]
Calculating \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]
Now substituting back into the energy equation:
\[ E = (9 \times 10^{-31} \, \text{kg}) \cdot (9 \times 10^{16} \, \text{m}^2/\text{s}^2) \]
\[ E = 8.1 \times 10^{-14} \, \text{J} \]

### Step 4: Convert energy from Joules to electron volts (eV)
To convert Joules to electron volts, we use the conversion factor \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ E = \frac{8.1 \times 10^{-14} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 5.06 \times 10^5 \, \text{eV} \]
Converting to mega electron volts (MeV):
\[ E \approx 0.506 \, \text{MeV} \]

### Final Answer
The energy released during the process of a neutron breaking into a proton and an electron is approximately **0.506 MeV**.