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 in a hydrogen atom is negative, not positive. This negativity arises from the electrostatic attraction between the electron and the nucleus, as described by the formula: \[ U = -\frac{k e^2}{r} \] where \( U \) represents potential energy, \( k \) is Coulomb's constant, \( e \) is the elementary charge, and \( r \) is the electron-nucleus separation. Because the electron is bound, \( U \) must be negative.
The total energy of a bound charged particle, like an electron in a hydrogen atom, is the sum of its kinetic and potential energies. For this electron, the total energy is negative because the absolute value of the potential energy exceeds that of the kinetic energy.
Consequently, the assertion (that potential energy is negative) is true, while the reason (that total energy of a bound charged particle is negative) is also true, although the provided explanation incorrectly implies the opposite for the assertion.

Therefore, the correct answer is (D): Assertion is false but the reason is true.