Why Do Some Objects Glow in the Dark

 

Understanding Atom

Electrons that are in their original orbital, they are said to be in the ground state. Electrons can jump from one orbital to another. When they jump from an orbital of lower energy to higher energy, they absorb a quantum of light. Such electrons are known as excited electrons and the process is known as excitation.

But when the excited electrons return to their ground state, they release a quantum of light.

The Glow

When light is shined on a glow-in-the-dark object, the electrons jump from their ground state to a higher energy orbital. After it is dark again, the electrons slowly jump back to their ground state, releasing quanta of light resulting in the characteristic glow.

Does that mean that a photon of any energy can be released after an excited electron returns to the ground state?
No.

The photon cannot have any amount of energy, because it jumps from one orbital to another and cannot stay between two orbitals.
It is like, a ball on a staircase can be on a stair but not between two stairs.

The energy of the photon can be calculated by some math:

n: Orbital Number
ℎ: Planck's Constant (6.626 ✕ 10⁻³⁴ Js)
c: Speed of causality (≈ 3.00 ✕ 10⁸ ms⁻¹)
λ: Wavelength in m

Eₙ= −2.18 ✕ 10⁻¹⁸ J
                 n²

E= ℎc
       λ

For eg: A Hydrogen Atom jumping from n=4 to n=2.

E₄= −2.18 ✕ 10⁻¹⁸ J
                  4²
    =−1.36 ✕ 10⁻¹⁹ J


E₂= −2.18 ✕ 10⁻¹⁸ J
                  2²
    =−5.45 ✕ 10⁻¹⁹ J

Since the answer which is the wavelength, can't be negative we will take the absolute value of E₄ and E₂.

ΔE=E₂−E₄
     =4.09 ✕ 10⁻¹⁹ J

Now finding the wavelength:

E = ℎc
        λ
λ = ℎc
       E
   = 6.626 ✕ 10⁻³⁴ Js ✕ 3.00 ✕ 10⁸ ms⁻¹
                        4.09 ✕ 10⁻¹⁹ J
   =4.86 ✕ 10⁻⁷ m
   =486 nm