Kinetic Energy

To solve this question, we need to understand the concepts of kinetic energy, potential energy, and total energy of an electron in an atomic orbit. According to quantum mechanics, particularly the Bohr model of the hydrogen atom, the relationship between the kinetic energy (K), potential energy (U), and total energy (E) of an electron in an orbit is given by:

• Total energy E = kinetic energy K + potential energy U .
• In the Bohr model, the total energy of an electron is always negative, and given as E = -\frac{e^2}{2a} , where a is the radius of the orbit.
• The kinetic energy K is always positive and equal in magnitude to the negative of the total energy: K = -E .
• The potential energy U is twice the total energy but negative: U = 2E .

Given that the total energy E = 3.4 \, \text{eV} , let's use these relationships to determine the kinetic and potential energies:

Step 1: Calculate Kinetic Energy (K)

From the relationship, K = -E .

Therefore, K = -3.4 \, \text{eV} . Hence, the kinetic energy is 3.4 eV (since energy is typically given as a positive value in this context).

Step 2: Calculate Potential Energy (U)

From the relationship, U = 2E .

Therefore, U = 2(3.4) = 6.8 \, \text{eV} , and since potential energy is negative, U = -6.8 \, \text{eV} .

Hence, the correct option is 3.4 eV, -6.8 eV.

Conclusion: The kinetic energy and potential energy of the electron are 3.4 eV and -6.8 eV, respectively, which matches the correct answer option.