Answer: The longest wavelength of light is 656.5 nm
Explanation:
For the longest wavelength, the transition should be from n to n+1, where: n = lower energy level
To calculate the wavelength of light, we use 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 of radiation
[tex]R_H[/tex] = Rydberg's Constant = [tex]1.096776\times 10^7m^{-1}[/tex]
[tex]n_f[/tex] = Higher energy level = [tex]n_i+1=(2+1)=3[/tex]
[tex]n_i[/tex]= Lower energy level = 2 (Balmer series)
Putting the values in above equation, we get:
[tex]\frac{1}{\lambda }=1.096776\times 10^7m^{-1}\left(\frac{1}{2^2}-\frac{1}{3^2} \right )\\\\\lambda =\frac{1}{1.5233\times 10^6m^{-1}}=6.565\times 10^{-7}m[/tex]
Converting this into nanometers, we use the conversion factor:
[tex]1m=10^9nm[/tex]
So, [tex]6.565\times 10^{-7}m\times (\frac{10^9nm}{1m})=656.5nm[/tex]
Hence, the longest wavelength of light is 656.5 nm
