What value of wavelength is associated with the Lyman series for n = 2? (R_H = 1.097*10⁷ m ^- ¹) A)8.2 * 10⁶ m B)1.2 *10 ^- ⁷ m C)2.7 * 10⁶ m D)3.6*10 ^- ⁷ m E)8.8 *10 ^- ⁷ m

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Quizplus · Accepted Answer

The Lyman series corresponds to transitions from higher energy levels to the n = 1 level. The formula for the wavelength of the Lyman series is given by 1/λ = R((1/n1^2) - (1/n2^2)), where R is the Rydberg constant (1.097x10^7/m), n1=1, and n2 is the higher energy level. For the n=2 to n=1 transition, we have n1=1 and n2=2, so 1/λ = R((1/1^2) - (1/2^2)), simplifying to 1/λ = (3/4)R. Plugging in the value of R, we get 1/λ = (3/4)(1.097x10^7/m), which simplifies to λ = 1.215x10^-7 m or 121.5 nm. In scientific notation, this is 1.2x10^-7 m, giving us choice (B).

What Value of Wavelength Is Associated with the Lyman Series