The total energy of an electron is 3.555 MeV, then its Kinetic energy is

Options

A. 3.545 MeV
B. 3.045 MeV
C. 3.5 MeV
D. None

Explanation

To find the kinetic energy of an electron given its total energy, we can use the relationship between total energy, kinetic energy, and rest mass energy. Here’s a step-by-step solution:

### Step 1: Understand the relationship between total energy, kinetic energy, and rest mass energy.
The total energy (E) of a particle is given by the formula:
\[ E = KE + E_0 \]
where:
- \( KE \) is the kinetic energy,
- \( E_0 \) is the rest mass energy.

### Step 2: Determine the rest mass energy of the electron.
The rest mass energy (\( E_0 \)) can be calculated using the formula:
\[ E_0 = m_0 c^2 \]
where:
- \( m_0 \) is the rest mass of the electron (approximately \( 9.1 \times 10^{-31} \) kg),
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s).

### Step 3: Calculate the rest mass energy in MeV.
First, we need to calculate \( E_0 \):
\[ E_0 = (9.1 \times 10^{-31} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]
Calculating this gives:
\[ E_0 = 9.1 \times 10^{-31} \times 9 \times 10^{16} \]
\[ E_0 \approx 8.19 \times 10^{-14} \text{ J} \]

Now, to convert joules to MeV, we use the conversion factor:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Thus,
\[ 1 \text{ MeV} = 10^6 \text{ eV} = 1.6 \times 10^{-13} \text{ J} \]
So,
\[ E_0 \approx \frac{8.19 \times 10^{-14}}{1.6 \times 10^{-13}} \text{ MeV} \approx 0.51 \text{ MeV} \]

### Step 4: Use the total energy to find the kinetic energy.
Given that the total energy \( E \) is \( 3.555 \text{ MeV} \):
\[ KE = E - E_0 \]
Substituting the values:
\[ KE = 3.555 \text{ MeV} - 0.51 \text{ MeV} \]
\[ KE = 3.045 \text{ MeV} \]

### Final Answer:
The kinetic energy of the electron is \( 3.045 \text{ MeV} \).

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