Question

An excited atom decays to its ground state and emits a photon of green light. If instead the atom decays to an intermediate state, then the light emitted could be

Answer 1

the light emitting must be of greater wavelength

Step-by-step explanation:

For this exercise we must use the Planck equation

E = h f

And the speed of light

c = λ f

f = c / λ

We replace

E = h c / λ

The wavelength of the green light is of the order of 500 nm, let's calculate the energy

E = 6.63 10⁻³⁴ 3 10⁸ /λ

E = 1,989 10⁻²⁵ /λ

λ = 500 nm = 500 10⁻⁹ m

E = 1,989 10⁻²⁵ / 500 10⁻⁹

E = 3,978 10⁻¹⁹ J

That is the energy of the transition for a transition is an intermediate state the energy must be less, this implies that the wavelength must increase. For the explicit case of a state with half of this energy

`E_(int)` = E / 2

`E_(int)` = 3,978 10⁻¹⁹ / 2 = 1,989 10⁻¹⁹

Let's clear and calculate

λ = h c / E

λ = 1,989 10⁻²⁵ / 1,989 10⁻¹⁹

λ = 1 10⁻⁶ m

Let's reduce to nm

λ = 1000 nm

This wavelength is in the infrared region

the light emitting must be of greater wavelength