Introduction:
A galvanic cell consists of two half-cells, each containing an electrode immersed in an electrolyte solution. The electrode at which reduction occurs is called the cathode, while the electrode at which oxidation occurs is called the anode. The emf (electromotive force) of a galvanic cell is a measure of the potential difference between the two electrodes.

Objective:
To determine the solution in which the other hydrogen electrode should be immersed to obtain the minimum emf in a galvanic cell.

Explanation:
In a galvanic cell, the emf is determined by the difference in potential between the two half-cells. The standard hydrogen electrode (SHE) is used as a reference electrode, and its potential is defined as zero. The potential of any other electrode is measured relative to the potential of the SHE.

Factors affecting the emf of a galvanic cell:
1. Concentration of the electrolyte solution: The concentration of the electrolyte solution affects the concentration of ions available for the redox reactions at the electrodes. This, in turn, affects the potential difference between the electrodes.

2. Nature of the electrolyte solution: The nature of the electrolyte solution determines the ions present in the solution, which can participate in redox reactions. Different ions have different redox potentials, which contribute to the overall potential difference of the cell.

3. Temperature: The temperature affects the rate of redox reactions and the mobility of ions in the electrolyte solution, which can influence the emf of the cell.

Determining the solution for minimum emf:
To achieve the minimum emf in the galvanic cell, we need to consider the redox potentials of the possible electrolyte solutions. The hydrogen electrode acts as an anode in the cell, undergoing oxidation according to the half-reaction: 2H⁺ + 2e⁻ → H₂.

Considering the given options:
(a) 0.1M HCl: The redox potential of HCl is relatively high, and it can easily react with the hydrogen electrode, resulting in a higher potential difference.

(b) 0.1M H2SO4: The redox potential of H2SO4 is also relatively high, and it can react with the hydrogen electrode, resulting in a higher potential difference.

(c) 0.1M NH4OH: The redox potential of NH4OH is lower compared to HCl and H2SO4. It is less likely to react with the hydrogen electrode, resulting in a lower potential difference.

(d) 0.01M HCOOH: The redox potential of HCOOH is lower compared to HCl and H2SO4 but higher than NH4OH. It is less likely to react with the hydrogen electrode compared to HCl and H2SO4 but more likely compared to NH4OH, resulting in an intermediate potential difference.

Conclusion:
To obtain the minimum emf in the galvanic cell, the other hydrogen electrode should be immersed in 0.1M NH4OH solution. This solution has a lower redox potential and is less likely to react with the hydrogen electrode, resulting in a lower potential difference.

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