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Change in Kinetic Energy of the Electron:
When an electron in an atom undergoes a transition, its kinetic energy can change. Let's assume the initial kinetic energy of the electron is represented as x.

Given:
The problem states that the kinetic energy changes from x to x/4.

Change in Potential Energy:
To determine the change in potential energy, we need to understand the relationship between kinetic and potential energy.

The Relationship between Kinetic and Potential Energy:
In an atom, the potential energy of an electron is negative and inversely proportional to its distance from the nucleus. As the electron moves closer to the nucleus, its potential energy decreases, and as it moves away, its potential energy increases.

Conservation of Energy:
According to the law of conservation of energy, the total energy of the system (kinetic energy + potential energy) remains constant. Therefore, any change in the kinetic energy of the electron must be accompanied by an equal and opposite change in its potential energy to maintain the total energy of the system.

Calculating the Change in Potential Energy:
1. Initial total energy = Initial kinetic energy + Initial potential energy = x + Initial potential energy
2. Final total energy = Final kinetic energy + Final potential energy = x/4 + Final potential energy
3. According to the law of conservation of energy, Initial total energy = Final total energy
4. Therefore, x + Initial potential energy = x/4 + Final potential energy
5. Rearranging the equation, Final potential energy = (x + Initial potential energy) - (x/4)

Interpreting the Result:
The expression (x + Initial potential energy) represents the initial total energy of the electron, while (x/4) represents the final kinetic energy. By subtracting the final kinetic energy from the initial total energy, we can determine the change in potential energy of the electron.

Conclusion:
The change in potential energy of the electron can be calculated using the equation Final potential energy = (x + Initial potential energy) - (x/4). The specific value of the change in potential energy depends on the initial potential energy of the electron and the initial kinetic energy of the system.