$\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ denote the populations of two energy states $\mathrm{E}_{\mathrm{A}}$ and $\mathrm{E}_{\mathrm{B}}$ and $\mathrm{E}_{\mathrm{A}}>\mathrm{E}_{\mathrm{B}}$, The correct statement when the temperature $\mathrm{T}_{1}>\mathrm{T}_{2}$ is
(a)$\mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{1}\right)>\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{1}\right), \mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{2}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{2}\right)$ and $\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{1}>\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{2}$
(b)$\mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{1}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{1}\right), \mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{2}\right)>\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{2}\right)$ and $\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{1}>\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{2}$
(c)$\mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{1}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{1}\right), \mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{2}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{2}\right)$ and $\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{1}>\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{2}$
(d)$\mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{1}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{1}\right), \mathrm{P}_{\mathrm{A}}\left(\mathrm{T}_{2}\right)<\mathrm{P}_{\mathrm{B}}\left(\mathrm{T}_{2}\right)$ and $\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{1}<\left(\mathrm{P}_{\mathrm{A}} / \mathrm{P}_{\mathrm{B}}\right) \mathrm{T}_{2}$
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
The higher level is always less populated (P_A < P_B at any T), and the ratio P_A/P_B = e^{−ΔE/kT} grows with temperature, so it is larger at T₁ > T₂.