Question Analysis: Assertion (A) and Reason (R) based on Bohr's Model of the Hydrogen Atom.
Step 1 (Formula / Governing Law): [0.25 Mark]
The electrostatic potential energy ($U$) of a system of two charges $q_1$ and $q_2$ separated by a distance $r$ is given by:
$$U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}$$For a hydrogen atom, the nucleus has charge $+Ze$ (where $Z=1$) and the electron has charge $-e$.
Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
- Substituting the charges into the formula: $U = \frac{1}{4\pi\epsilon_0} \frac{(+e)(-e)}{r} = -\frac{1}{4\pi\epsilon_0} \frac{e^2}{r}$
- Since $e^2$, $r$, and $\epsilon_0$ are all positive quantities, the potential energy $U$ is negative.
- Regarding the Reason (R): The total energy ($E$) of a bound system (like an electron in an atom) is negative ($E = K + U < 0$). Therefore, the statement that total energy is "always positive" is factually incorrect.
Step 3 (Final Concluded Answer): [0.25 Mark]
Conclusion: Both Assertion (A) and Reason (R) are False.
💡 EL10 Concept Insight: Think of the electron as being trapped in a "gravity well" created by the positive nucleus; because it needs energy to escape this trap, its energy state is considered "negative" (like being in a hole), not positive.