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

The potential energy of an electron revolving in a hydrogen atom is negative, not positive. This is because the electron is bound to the nucleus by the electrostatic force, and the potential energy is given by: \[ U = -\frac{k e^2}{r} \] where \( U \) is the potential energy, \( k \) is Coulomb's constant, \( e \) is the electron charge, and \( r \) is the distance between the electron and the nucleus. Since the electron is bound, \( U \) is negative.
However, the total energy of a charged particle, such as the electron in a hydrogen atom, is the sum of its kinetic energy and potential energy. For the electron in a hydrogen atom, the total energy is negative because the magnitude of the potential energy is greater than the kinetic energy in magnitude.
Thus, the assertion is false (the potential energy is negative), while the reason is true (the total energy of a charged particle is always negative in bound states, but the reason is about total energy being negative, not positive).
Therefore, the correct answer is (D): Assertion is false but the reason is true.