The wavelength of a photon that the hydrogen atom emits is 1.093 x 10^-8 m.
The wavelength of a photon is given by the following formula,
1/λ = R{1/n1^2- 1/n2^2}
Here λ is the wavelength of the photon
R is the Rydberg Constant= 1.097 x 10^7 m
N1 is the initial state
N2 is the final state
Putting n1 =3, n2= 6 in the above equation, the wavelength lambda comes out to be,
1/λ = R{1/(3)^2 - 1/(6)^2}
λ = 12/1.097 x 10^7
Lambda = 1.093 x 10^-8 m.
Hence, the wavelength of the photon that the hydrogen atom emits is 1.093 x 10^-8 m.
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