Calculating Total Electron Energy from Kinetic Energy

This problem asks for the total energy of an electron, given a value of 3.53 MeV. Based on the options and standard physics principles, we can infer that 3.53 MeV represents the kinetic energy ($K$) of the electron, and we need to calculate the total energy ($E$).

Understanding Electron Energy Components

The total energy of a particle, like an electron, is composed of its rest energy and its kinetic energy.

• Rest Energy ($E_0$): This is the energy an object possesses due to its mass alone. For an electron, this is a well-known constant.
• Kinetic Energy ($K$): This is the energy an object possesses due to its motion.
• Total Energy ($E$): This is the sum of the rest energy and the kinetic energy.

Key Values and Formula

• The rest energy of an electron ($E_0$) is approximately 0.511 MeV.
• The kinetic energy ($K$) given in the problem is 3.53 MeV.
• The formula relating these energies is: $$E = E_0 + K$$

Step-by-Step Calculation

1. Identify the known values:
   • Rest Energy ($E_0$): $0.511 \text{ MeV}$
   • Kinetic Energy ($K$): $3.53 \text{ MeV}$
2. Apply the total energy formula: $$E = E_0 + K$$
3. Substitute the values into the formula: $$E = 0.511 \text{ MeV} + 3.53 \text{ MeV}$$
4. Calculate the sum: $$E = 4.041 \text{ MeV}$$
5. Round the result to match the options: $$E \approx 4.04 \text{ MeV}$$

Conclusion

By adding the electron's rest energy to its kinetic energy, we find the total energy. The calculated total energy is approximately 4.04 MeV.