Find the rest mass energy of electron.

Options

A. 0.8 MeV
B. 1.66 amu
C. 0.519 MeV
D. None of these

Explanation

To find the rest mass energy of an electron, we can follow these steps:

### Step 1: Understand the formula for rest mass energy
The rest mass energy (E) of an object is given by the equation:
\[ E = mc^2 \]
where:
- \( m \) is the rest mass of the object,
- \( c \) is the speed of light in a vacuum.

### Step 2: Identify the mass of the electron
The rest mass of the electron is:
\[ m = 9.1 \times 10^{-31} \text{ kg} \]

### Step 3: Identify the speed of light
The speed of light is:
\[ c = 3 \times 10^8 \text{ m/s} \]

### Step 4: Substitute the values into the formula
Now, substitute the values of \( m \) and \( c \) into the equation:
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

### Step 5: Calculate \( c^2 \)
First, calculate \( c^2 \):
\[ c^2 = (3 \times 10^8 \text{ m/s})^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 6: Calculate the rest mass energy in joules
Now substitute \( c^2 \) back into the equation for \( E \):
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (9 \times 10^{16} \text{ m}^2/\text{s}^2) \]
\[ E = 8.19 \times 10^{-14} \text{ J} \]

### Step 7: Convert joules to electron volts
To convert joules to electron volts, use the conversion factor:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Thus, to convert \( E \) from joules to electron volts:
\[ E \text{ (in eV)} = \frac{E \text{ (in J)}}{1.6 \times 10^{-19} \text{ J/eV}} \]
\[ E \text{ (in eV)} = \frac{8.19 \times 10^{-14} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} \]

### Step 8: Perform the division
Calculating this gives:
\[ E \text{ (in eV)} = 5.11875 \times 10^5 \text{ eV} \]
or in mega electron volts (MeV):
\[ E \text{ (in MeV)} = 0.511875 \text{ MeV} \]

### Final Answer
The rest mass energy of the electron is approximately:
\[ E \approx 0.511 \text{ MeV} \]

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