Respuesta :
Answer : The initial and final values of the quantum number is, 2 and 3
Explanation :
Assumption : We have to determine the value of wavelength when electron will jump from 2 to 3 level.
Using Rydberg's Equation:
[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )[/tex]
Where,
[tex]\lambda[/tex] = Wavelength
[tex]R_H[/tex] = Rydberg's Constant = [tex]1.097\times 10^7m^{-1}[/tex]
[tex]n_f[/tex] = Higher energy level = 3
[tex]n_i[/tex]= Lower energy level = 2
Putting the values, in above equation, we get
[tex]\frac{1}{\lambda}=(1.097\times 10^7m^{-1})\left(\frac{1}{2^2}-\frac{1}{3^2} \right )[/tex]
[tex]\frac{1}{\lambda}=(1.097\times 10^7m^{-1})\left(\frac{1}{4}-\frac{1}{9} \right )[/tex]
[tex]\frac{1}{\lambda}=1523611.111m^{-1}[/tex]
[tex]\lambda=6.563\times 10^{-7}m[/tex]
[tex]\lambda=656.3\times 10^{-9}m[/tex]
[tex]\lambda=656.3nm[/tex]
From this we conclude that the calculated value of wavelength is equal to given value of wavelength.
Therefore, the initial and final values of the quantum number is, 2 and 3
