Answer: The maximum wavelength of light that can be emitted is [tex]1.9\times 10^{-6}m[/tex]
Explanation:
[tex]E=\frac{hc}{\lambda}[/tex]
[tex]\lambda[/tex] = Wavelength of radiation
E= energy
For wavelength to be maximum, energy would be minimum, i.e the electron will jump from n=4 level to n =3
Using Rydberg's Equation:
[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )\times Z^2[/tex]
Where,
[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 = 4
Z= atomic number = 1 (for hydrogen)
[tex]\frac{1}{\lambda}=1.097\times 10^7\left(\frac{1}{3^2}-\frac{1}{4^2} \right )\times 1^2[/tex]
[tex]\frac{1}{\lambda}=0.053\times 10^7[/tex]
[tex]\lambda=1.9\times 10^{-6}m[/tex]
Thus the maximum wavelength of light that can be emitted is [tex]1.9\times 10^{-6}m[/tex]