Two aqueous $1:1$ electrolyte systems A and B are at different temperatures $\mathrm{T_A}$ and $\mathrm{T_B}$ and $\mathrm{C_A}$ and $\mathrm{C_B}$ concentrations, respectively. Their Debye lengths will be equal if
(c)$\mathrm{T_A}=\sqrt{2}\,\mathrm{T_B}$ and $\mathrm{C_A}=2\mathrm{C_B}$
(a)$\mathrm{T_A}=2\mathrm{T_B}$ and $\mathrm{C_A}=2\mathrm{C_B}$
(b)$\mathrm{T_A}=2\mathrm{T_B}$ and $\mathrm{C_A}=\mathrm{C_B}/2$
(d)$\mathrm{T_A}=2\mathrm{T_B}$ and $\mathrm{C_A}=\sqrt{2}\,\mathrm{C_B}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
Debye length ∝ √(εT/I); for 1:1 electrolytes I = c, so equality needs T_A/c_A = T_B/c_B, e.g. T_A = 2T_B with c_A = 2c_B.