The rest energy of an electron is.

Options

A. 510 KeV
B. 931 KeV
C. 510 MeV
D. 931 MeV

Answer

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

### Step 1: Identify the mass of the electron
The mass of the electron (\(m_e\)) is given as:
\[ m_e = 9.1 \times 10^{-31} \text{ kg} \]

### Step 2: Use the mass-energy equivalence formula
According to Einstein's mass-energy equivalence principle, the rest energy (\(E\)) can be calculated using the formula:
\[ E = m_e c^2 \]
where \(c\) is the speed of light in a vacuum.

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

### Step 4: Calculate \(c^2\)
Now, we calculate \(c^2\):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

### Step 5: Substitute the values into the energy equation
Now we substitute \(m_e\) and \(c^2\) into the energy equation:
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (9 \times 10^{16} \text{ m}^2/\text{s}^2) \]

### Step 6: Perform the multiplication
Calculating the above expression:
\[ E = 8.19 \times 10^{-14} \text{ J} \]

### Step 7: Convert Joules to electron volts
To convert energy from Joules to electron volts (eV), we use the conversion factor:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Thus, we convert:
\[ E (\text{in eV}) = \frac{8.19 \times 10^{-14} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} \approx 5.11875 \times 10^5 \text{ eV} \]

### Step 8: Round to appropriate significant figures
Rounding this value gives:
\[ E \approx 510 \text{ keV} \]

### Final Answer
The rest energy of an electron is approximately:
\[ \boxed{510 \text{ keV}} \]

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