Answer:
The energy is [tex]E = 2.08*10^{-19}J[/tex]
Explanation:
From the question we are told that
The energy level of the photon is [tex]n=8[/tex]
Generally the spatial frequency([tex]\frac{1}{\lambda}[/tex]) of this transition is mathematically represented as
[tex]\frac{1}{\lambda } = R * (\frac{1}{n_1} - \frac{1}{n} )[/tex]
Where R is the Rydberg constant with a value of [tex]1.09 * 10^7m^{-1}[/tex]
[tex]n_1[/tex] is the principle quantum number for Paschen series with value given a s [tex]n_1 = 3[/tex]
[tex]\lambda[/tex] is the wavelength of the photon
Now substituting values
[tex]\frac{1}{\lambda } = 1.097 *10^7 (\frac{1}{3^2} - \frac{1}{8^2} )[/tex]
[tex]= 1.047 *10^6m^{-1}[/tex]
Now the energy of this photon is mathematically represented as
[tex]E = h * c * \frac{1}{\lambda}[/tex]
where h is the Planck's constant with value [tex]h = 6.626 *10 ^ {-34} J \cdot sec[/tex]
c is the speed of light with value [tex]c = 3.0*10^8 m/s[/tex]
Substituting values
[tex]E = 6.626 *10^{-34} * 3*10^8 * 1.047 *10^6[/tex]
[tex]= 2.08*10^{-19}J[/tex]
