The allowed energies of a quantum system are 0.0 ev, 5.0 ev , and 8.5 ev .
what wavelengths appear in the system's emission spectrum?
express your answers in nanometers in ascending order separated by commas.

Explanation:

Given that,

Energies of a quantum system

E₁ = 0.0 eV

E₂ = 5.0 eV

E₃ = 8.5 eV

We need to calculate the wavelength

Using formula of energy

An electron transits from 5.0 eV to 0.0 eV

Thereby emitting a photon

For E₁ = 5.0 eV,

Using formula of energy

Where, E = energy

h = Planck constant

= wavelength

Put the value into the formula

An electron transits from 8.5 eV to 0.0 eV

Thereby emitting a photon

For E₂ = 8.5 eV,

The wavelength of photon

An electron transits from 8.5 eV to 5.0 eV

Thereby emitting a photon

For E₃ = 8.5-5.0 =3.5 eV,

The wavelength of photon

Hence, This is the required solution.

6 cos 34, 6 sin 34 trig