Rydberg's Equation

[WilliamNguyen_4L]

Why in the equation ΔE=Rhc((1/nf^2)−(1/ni^2)) is nf always the smaller of the two energy levels?

[Timothy_Yueh_4L]

Since it is 1/nf^2 – 1/ni^2, the resulting energy value is positive if nf is the smaller value. Since delta E represents the change of energy, which tends to be a positive value, nf needs to be the smaller primary quantum number in order to satisfy that condition.