The wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3 is 1282 nm.
From the Rydberg's formula;
1/λ = R (1/[tex]n^{2} _{final}[/tex] - 1/[tex]n^{2} _{initial}[/tex])
R = 1.097 ×[tex]10^{7} m^{-1}[/tex]
nfinal = 3
ninitial = 5
Calculating the wavelength of the photon by substituting values, in equation 1/λ = R (1/[tex]n^{2} _{final}[/tex] - 1/[tex]n^{2} _{initial}[/tex]) , we get:
1/λ = 1.096776×[tex]10^{7} m^{-1}[/tex] (1/[tex]3^{2}[/tex] - 1/[tex]5^{2}[/tex])
1/λ = 1.096776×[tex]10^{7} m^{-1}[/tex] (1/9 - 1/25)
λ = 1.282 × [tex]10^{-6}[/tex] m
λ = 1282 nm
Therefore, the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3 is 1282 nm.
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