Answer: The wavelength of the photon is 486.2 nm and it lies in the visible region
Explanation:
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]1.097\times 10^7m^{-1}[/tex]
[tex]n_f[/tex] = Higher energy level = 4
[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}{4^2} \right )\\\\\lambda =4.862\times 10^{-7}m[/tex]
Converting this into nanometers, we use the conversion factor:
[tex]1m=10^9nm[/tex]
So, [tex]4.862\times 10^{-7}m\times (\frac{10^9nm}{1m})=486.2nm[/tex]
As, the range of wavelength of visible light is 400 nm - 700 nm. So, the wavelength of the given photon lies in the visible region
Hence, the wavelength of the photon is 486.2 nm and it lies in the visible region
