Final answer:
The wavelength of light emitted when an excited electron in the hydrogen atom falls from n=5 to n=2 is approximately 434 nm.
Step-by-step explanation:
The wavelength of light emitted when an excited electron in the hydrogen atom falls from n=5 to n=2 can be calculated using the Rydberg formula:
1/λ = R (1/nf^2 - 1/ni^2)
where λ is the wavelength, R is the Rydberg constant (approximately 1.097 x 10^7 m^-1), and nf and ni are the final and initial energy levels respectively.
Substituting the values nf=2 and ni=5 into the formula, we get:
1/λ = 1.097 x 10^7 (1/2^2 - 1/5^2)
Simplifying the equation gives us:
1/λ = 1.097 x 10^7 (1/4 - 1/25)
1/λ = 1.097 x 10^7 (21/100)
1/λ = 1.097 x 10^7 x 0.21
1/λ = 2.3027 x 10^6
Using the reciprocal of both sides:
λ = 4.34 x 10^-7 m
Converting to nanometers (nm), the wavelength is approximately 434 nm.