**Kinetic Energy of an Electron in the nth Shell**

The kinetic energy of an electron in the nth shell can be determined using the formula:

KE = (1/2)mv²

Where:
- KE is the kinetic energy
- m is the mass of the electron
- v is the velocity of the electron

In the context of an electron in the nth shell, the mass of the electron remains constant regardless of the shell it occupies. Therefore, the kinetic energy of the electron mainly depends on its velocity.

**Potential Energy in the Same Shell**

The potential energy of an electron in the same shell can be calculated using the formula:

PE = -eV

Where:
- PE is the potential energy
- e is the charge of the electron
- V is the electric potential

In an atom, the electric potential is determined by the attractive force between the positively charged nucleus and the negatively charged electrons. As the electron moves away from the nucleus, the electric potential energy increases, and as it moves closer, the potential energy decreases.

**Relationship Between Kinetic and Potential Energy**

In an atom, the total energy of an electron is the sum of its kinetic energy and potential energy. According to the conservation of energy, the total energy of the electron remains constant.

Therefore, we can express the relationship between kinetic and potential energy as:

Total Energy (E) = KE + PE

Since the total energy remains constant, any change in the kinetic energy of the electron will be compensated by an equal and opposite change in the potential energy.

**Conclusion**

In conclusion, the potential energy of an electron in the nth shell can be determined by subtracting its kinetic energy from the total energy. The relationship between kinetic and potential energy is such that any change in the kinetic energy of the electron is balanced by an equal and opposite change in the potential energy.

-x/2