Respuesta :
Answer: Wavelength of light emitted when the electron in doubly ionized lithium makes a transition from E12 to E8 is [tex]0.1050\times 10^{-4m[/tex]
Explanation:
[tex]Li:3:1s^22s^1[/tex]
[tex]Li^{2+}:1:1s^1[/tex]
Using Rydberg's Equation for hydrogen and hydrogen like atom:
[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )[/tex]
Where,
[tex]\lambda[/tex] = Wavelength of radiation
[tex]R_H[/tex] = Rydberg's Constant
[tex]n_f[/tex] = Higher energy level
[tex]n_i[/tex]= Lower energy level
We have:
[tex]n_f=8, n_i=12[/tex]
[tex]R_H=1.097\times 10^7 m^{-1}[/tex]
[tex]\frac{1}{\lambda}=1.097\times 10^7 m^{-1}\times \left(\frac{1}{12^2}-\frac{1}{8^2} \right )[/tex]
[tex]\frac{1}{\lambda}=1.097\times 10^7 m^{-1}\times \frac{5}{576}[/tex]
[tex]\frac{1}{\lambda}=9.523\times 10^4 m[/tex]
[tex]\frac{1}{\lambda}=9.523\times 10^4 m[/tex]
[tex]{\lambda}=0.1050\times 10^{-4}m[/tex]
The wavelength of the photon emitted when the hydrogen atom undergoes a transition is [tex]0.1050\times 10^{-4m[/tex]
