Assume that a neutron breaks into a proton and an electron. The energy released 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
We have the following masses:
- Mass of neutron, \( m_n = 1.6725 \times 10^{-27} \) kg
- Mass of proton, \( m_p = 1.6725 \times 10^{-27} \) kg
- Mass of electron, \( m_e = 9 \times 10^{-31} \) kg

### Step 2: Calculate the change in mass (\( \Delta m \))
The change in mass during the decay process can be calculated using the formula:
\[ \Delta m = m_n - (m_p + m_e) \]
Substituting the values:
\[ \Delta m = 1.6725 \times 10^{-27} - (1.6725 \times 10^{-27} + 9 \times 10^{-31}) \]
This simplifies to:
\[ \Delta m = 1.6725 \times 10^{-27} - 1.6725 \times 10^{-27} - 9 \times 10^{-31} = -9 \times 10^{-31} \text{ kg} \]
Since we are interested in the absolute value of the mass defect:
\[ \Delta m = 9 \times 10^{-31} \text{ kg} \]

### Step 3: Calculate the energy released (\( E \))
Using Einstein's mass-energy equivalence principle, the energy released can be calculated using the formula:
\[ E = \Delta m c^2 \]
Where \( c \) (the speed of light) is approximately \( 3 \times 10^8 \) m/s. Substituting the values:
\[ E = (9 \times 10^{-31}) \times (3 \times 10^8)^2 \]
Calculating \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
Now substituting this back into the energy equation:
\[ E = 9 \times 10^{-31} \times 9 \times 10^{16} = 81 \times 10^{-15} \text{ J} \]

### Step 4: Convert energy from Joules to electron volts
To convert Joules to electron volts, we use the conversion factor \( 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \):
\[ E (\text{eV}) = \frac{81 \times 10^{-15}}{1.6 \times 10^{-19}} \approx 506.25 \times 10^{4} \text{ eV} \]
This can be simplified to:
\[ E \approx 5.0625 \times 10^{5} \text{ eV} = 506.25 \text{ keV} \]

### Step 5: Convert keV to MeV
Since \( 1 \text{ MeV} = 1000 \text{ keV} \):
\[ E \approx 0.50625 \text{ MeV} \]

### Step 6: Round to the nearest option
The nearest option to \( 0.50625 \text{ MeV} \) is \( 0.57 \text{ MeV} \).

### Final Answer
The energy released during the process is approximately \( 0.57 \text{ MeV} \).

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