Intensity Concentration Relationship:

The intensity of the emitted radiation (P) is proportional to the number of excited atoms N*.

P ∝ N*

P = a. N* (where a is the proportionality constant)

Again, from Eq, we see that the number of atoms in the excited state, N*, at a given temperature are proportional to N₀. Thus, we can write the following.

P = a.  N₀ =g*/g₀e^-ΔE/kT( as N* = N₀ =g*/g₀e^-ΔE/kT)

P = K. N₀(K=a. g*/g₀e^-ΔE/kT)

P = K′. C (as, N₀ is directly proportional to metal concentration) Therefore, the intensity of the emitted light will be directly proportional to the concentration of the element introduced within the flame.