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State and explain the formula that gives wavelengths of lines in the hydrogen spectrum.

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Formula : \(\cfrac1λ\) = R \(\left[\cfrac{1}{n^2}-\cfrac1{m^2}\right]\)

where λ is the wavelength of a line in the hydrogen spectrum, R is a constant, now called the Rydberg constant, and n and m are integers with n = 1,2,3,… and m = n + 1, n + 2, n + 3, For a fixed value of n, λ decreases as m increases and has minimum value as m → ∞ λ = \(\cfrac{n^2}R\) as

Lyman, Balmer and Paschen series in the hydrogen spectrum (For reference only) 

[Note : A line spectrum is atomic in origin. It is a signature of the element, i.e., we can determine the elements present in a mixture of elements by studying the line spectrum of the mixture.]

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