Question

Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive. 
Reason (R): The total energy of a charged particle is always positive.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false and Reason (R) is also false.

Hint:

In a hydrogen atom, the potential energy of the electron is negative, not positive. The total energy of a bound charged particle is also negative.

Answer 1

The Correct Option is D

Evaluation of statements regarding an electron in a hydrogen atom:

Assertion (A): The potential energy of an electron in any stationary orbit of a hydrogen atom is positive.

Reason (R): The total energy of a charged particle is invariably positive.

Analysis of atomic energy concepts:

• Potential energy (PE) of an electron in a hydrogen atom is negative due to the attractive Coulomb force between the electron and the nucleus. The expression for potential energy is PE = −ke²/r, where k is Coulomb’s constant, e is the electronic charge, and r is the orbital radius. The negative sign indicates attraction.
• The total energy (E) of an electron in a bound state, such as a hydrogen atom, is also negative. It is the sum of kinetic energy (KE) and potential energy (PE), given by E = KE + PE. For bound systems, the total energy is less than zero.

Findings:

• Assertion (A) is false because the potential energy of an electron in a stationary orbit is negative.
• Reason (R) is false because the total energy of a charged particle in a bound system is not always positive.

Conclusion:
Assertion (A) is false and Reason (R) is also false.