The distance between identical points in adjacent cycles of a waveform signal is called wavelength. The n₁ for the initial level of the electron is 4.
The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal carried in space or down a wire is defined as the wavelength.
Given the wavelength is 489.2 nm, also, it is stated that the nf level is Balmer series. Therefore,
nf level = 2
The wavelength, λ = 489.2 nm = 4.86× 10⁻⁷ meter
Now, the mathematical formula for wavelength is given as,
[tex]\dfrac{1}{\lambda} = R[\dfrac{1}{nf^2}-\dfrac{1}{n_1^2}][/tex]
where R is the Rydberg constant and its value is equal to 1.097×10⁷.
Therefore, we can write,
[tex]\dfrac{1}{4.86 \times 10^{-7}} = 1.097 \times 10^7 [\dfrac{1}{2^2} - \dfrac{1}{n_1^2}][/tex]
n₁ = 4.0021 ≈ 4
Hence, the n₁ for the initial level of the electron is 4.
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