A variable, the opposite external potential $$(E_{ext})$$ is applied to the cell Zn | Zn$$^{2+}$$ (1M) || Cu$$^{2+}$$ (1M) | Cu, of potential 1.1 V. When $$E_{ext} < 1.1$$ V and $$E_{ext} > 1.1$$ V, respectively electrons flow from

The given cell is Zn | Zn²⁺ (1M) || Cu²⁺ (1M) | Cu with a standard cell potential of 1.1 V. In this galvanic cell, zinc (Zn) acts as the anode and copper (Cu) acts as the cathode. The spontaneous reaction is: Zn → Zn²⁺ + 2e⁻ at the anode and Cu²⁺ + 2e⁻ → Cu at the cathode. Therefore, electrons naturally flow from the anode (Zn) to the cathode (Cu).

An external potential $$E_{ext}$$ is applied in the opposite direction to the cell potential. The net cell potential $$E_{net}$$ is given by $$E_{net} = E_{cell} - E_{ext}$$, where $$E_{cell} = 1.1$$ V.

Case 1: When $$E_{ext} < 1.1$$ V
Here, $$E_{net} = 1.1 - E_{ext}$$. Since $$E_{ext} < 1.1$$ V, $$E_{net} > 0$$. The net potential is positive, so the cell behaves as a galvanic cell, and the spontaneous reaction continues. Electrons flow from the anode (Zn) to the cathode (Cu).

Case 2: When $$E_{ext} > 1.1$$ V
Here, $$E_{net} = 1.1 - E_{ext}$$. Since $$E_{ext} > 1.1$$ V, $$E_{net} < 0$$. The net potential is negative, meaning the external potential overcomes the cell potential and drives the reaction in reverse. The cell now acts as an electrolytic cell. The reverse reaction occurs: Cu → Cu²⁺ + 2e⁻ (oxidation) at the copper electrode, making it the anode, and Zn²⁺ + 2e⁻ → Zn (reduction) at the zinc electrode, making it the cathode. Therefore, electrons flow from the copper electrode (which was originally the cathode) to the zinc electrode (which was originally the anode). In terms of the original labels, electrons flow from cathode to anode.

Summarizing:
- When $$E_{ext} < 1.1$$ V: electrons flow from anode to cathode.
- When $$E_{ext} > 1.1$$ V: electrons flow from cathode to anode.

Now, comparing with the options:
A. anode to cathode in both cases → Incorrect, as flow direction changes.
B. anode to cathode and cathode to anode → Correct, matches both cases.
C. cathode to anode and anode to cathode → Incorrect, reverses the flow order.
D. cathode to anode in both cases → Incorrect, only true for second case.

Hence, the correct answer is Option B.