Answer: The wavelength of light is 1281.9 nm
Explanation:
To calculate the wavelength of light, we use Rydberg's Equation:
[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_f^2}-\frac{1}{n_i^2} \right )[/tex]
Where,
[tex]\lambda[/tex] = Wavelength of radiation
[tex]R_H[/tex] = Rydberg's Constant = [tex]1.097\times 10^7m^{-1}[/tex]
[tex]n_f[/tex] = Upper energy level = 3
[tex]n_i[/tex]= Lower energy level = 5
Putting the values in above equation, we get:
[tex]\frac{1}{\lambda }=1.097\times 10^7m^{-1}\left(\frac{1}{3^2}-\frac{1}{5^2} \right )\\\\\lambda =\frac{1}{780089m^{-1}}=1.28\times 10^{-6}m[/tex]
Converting this into nanometers, we use the conversion factor:
[tex]1m=10^9nm[/tex]
So, [tex]1.2819\times 10^{-6}m\times (\frac{10^9nm}{1m})=1281.9nm[/tex]
Hence, the wavelength of light is 1281.9 nm
