The wavelength of the series limit (longest wavelength limit, i.e., the convergence limit) of the Lyman series of hydrogen is x angstrom. Calculate the wave number (in angstrom⁻¹) of the third line of the Balmer series of He+ ion.

Question

Accepted Answer

25 / (21x). The Lyman series limit wavelength of H is given by 1/x = R_H*(1/1² - 0) => R_H = 1/x. For He+ (Z=2), the third line of the Balmer series corresponds to n=5 -> n=2 transition. Wave number = R_H*Z²*(1/2² - 1/5²) = (1/x)*4*(25-4)/100 = (4*21)/(100x) = 84/(100x) = 21/(25x).

The wavelength of the series limit (longest wavelength limit, i.e., the convergence limit) of the Lyman series of hydrogen is x angstrom. Calculate the wave number (in angstrom⁻¹) of the third line of the Balmer series of He+ ion.

Solution

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