Question

explain the physical significance of a negative value for ΔE. why must E photon always be positive, while ΔE can be negative or positive?

Answer 1

The energy of a photon is given by hv, where h is Planck's constant and v is frequency.

h is positive and v is also positive, hence the energy of photon E will always be positive.

delta E can be positive or negative. When an electron in an atom/molecule jumps from high energy state to low energy state E2-E1 will be postive. But when electron has to go from low energy to high energy state it has to absorb light. Delta E = E1-E2, in that case will be negative.