Question

As an electron is brought from an infinite distance close to the nucleus of the atom, the energy of the electron-nucleus system:
(A) Increases to a greater positive value
(B) Decreases to a smaller positive value
(C) Increases to a greater negative value
(D) Decreases to a smaller negative value

Answer 1

Hint: When an electron is brought close to the nucleus, a repulsion takes place. Energy gets released in this process. So the net energy can be written as the Initial Energy- Final released energy.

Complete step by step solution:
The nucleus of an electron is filled with electrons in the outer part. Electrostatic energy of an electron depends on the square of the distance of the charges. It is inversely proportional to the square of the distance between the charges. Mathematically,
\[E\propto \left( \dfrac {1}{{r}^{2}} \right)\] ,
where E is electrostatic energy and r is the distance between the nucleus and electron.
At an infinite distance, r= infinity, so E will be equal to 0.
As the electron comes close to the nucleus, energy gets released. Release of energy implies that there is a decrease in energy going on in the system. The electron gets bound from the nucleus as it comes near. As the distance decreases, according to the formula, the energy increases, and since energy is released, the sign of the magnitude of energy is negative. The potential energy decreases and the Kinetic Energy increases, on approaching the nucleus. Hence, the energy increases to a greater negative value.

Note: Try not to make errors at the sign of energy. Remember that when an electron is approaching the nucleus, the energy is increasing as the distance is decreasing, but as energy is getting released, it will be denoted by a negative sign, and vice-versa.