Answer: The wavelength of light emitted is 434 nm
Explanation:
To calculate the wavelength of light, we use Rydberg's Equation:
\(\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )\)
Where,
\(\lambda\) = Wavelength of radiation
\(R_H\) = Rydberg's Constant = \(1.097\times 10^7m^{-1}\)
\(n_f\) = final energy level = 2
\(n_i\)= initial energy level = 5
Putting the values in above equation, we get:
\(\frac{1}{\lambda }=1.097\times 10^7m^{-1}\left(\frac{1}{5^2}-\frac{1}{2^2} \right )\\\\\lambda =\frac{1}{-2.304\times 10^6m^{-1}}=-4.34\times 10^{-7}m\)
As, the electron is getting emitted from n = 5 to n = 2. So, the wavelength will come out to be negative because it is getting emitted.
Converting this into nanometers, we use the conversion factor:
\(1m=10^9nm\)
So, \(4.34\times 10^{-7}m\times (\frac{10^9nm}{1m})=434nm\)
Hence, the wavelength of light emitted is 434 nm