You have acquired a spectrum of a hot star and see a line se

You have acquired a spectrum of a hot star and see a line series from a multiply ionized atom in your data. You didn’t bring your CRC Handbook of Chemistry with you to the telescope so you decide to make a guess at what it might be. your only way to tackle this problem is to assume the ion has been multiply ionized to the point where you can use the Bohr model to examine the spectral properties. Recall that a line series is a set of spectral lines that correspond to a set of transitions that terminate in the same final state. The longest and shortest  wavelengths of the series are 63.3 nm and 22.8 nm, respectively. What is the ion?

Solution

n_f / n_f + 1 = sqrt [1 - lambda_s / lambda_l]

= sqrt [1 - 22.8/ 63.3] = 0.799 = 0.800

n_f / n_f + 1 = 0.800, n_f = 4

Z = sqrt [n_f² / R lambda_s] = sqrt [4² / (1.097 * 10⁷ * 22.8 nm)] = 8

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The nearest three lines will come form transition from n = 6, 7, 8 to n = 4

lambda = 1/(Z² R) [1/n_f² - n_i²]^-1

lambda₁ = (1.42 * 10^-9)[1/4² - 6²]^-1

= 41 nm

lambda₂ = (1.42 * 10^-9)[1/4² - 7²]^-1

= 34 nm

lambda₃ = (1.42 * 10^-9)[1/4² - 8²]^-1

= 30.4 nm