Respuesta :
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
[tex]E=\dfrac{hc}{\lambda}[/tex]
An electron transits from 5.0 eV to 0.0 eV
Thereby emitting a photon
For E₁ = 5.0 eV,
Using formula of energy
[tex]E_{1}=\dfrac{hc}{\lambda_{1}}[/tex]
Where, E = energy
h = Planck constant
[tex]\lambda[/tex] = wavelength
Put the value into the formula
[tex]5.0\times1.6\times10^{-19}=\dfrac{6.63\times10^{-34}\times3\times10^{8}}{\lambda_{1}}[/tex]
[tex]\lambda_{1}=\dfrac{6.63\times10^{-34}\times3\times10^{8}}{5.0\times1.6\times10^{-19}}[/tex]
[tex]\lambda_{1}=2.486\times10^{-7}\ m[/tex]
[tex]\lambda_{1}=248.6\ nm[/tex]
An electron transits from 8.5 eV to 0.0 eV
Thereby emitting a photon
For E₂ = 8.5 eV,
The wavelength of photon
[tex]\lambda_{2}=\dfrac{6.63\times10^{-34}\times3\times10^{8}}{8.5\times1.6\times10^{-19}}[/tex]
[tex]\lambda_{2}=1.463\times10^{-7}\ m[/tex]
[tex]\lambda_{2}=146.3\ nm[/tex]
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
[tex]\lambda_{3}=\dfrac{6.63\times10^{-34}\times3\times10^{8}}{3.5\times1.6\times10^{-19}}[/tex]
[tex]\lambda_{3}=3.5517\times10^{-7}[/tex]
[tex]\lambda_{3}=355.2\ nm[/tex]
Hence, This is the required solution.
