What is the difference in wavelength for spectral lines emitted by hydrogen for transitions from the n = 16 level to the n = 2 level and transitions from the n = 15 level to the n = 2 level? (R_H = 1.097 *10⁷ m ^- ¹. ) A)1.0 *10 ^- ¹⁰ m B)2.0 *10 ^- ¹⁰ m C)4.1 *10 ^- ¹⁰ m D)8.1 *10 ^- ¹⁰ m E)1.6 *10 ^- ⁹ m

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Quizplus · Accepted Answer

The difference in wavelength for spectral lines emitted by hydrogen for transitions from the n = 16 level to the n = 2 level and transitions from the n = 15 level to the n = 2 level is given by:$$\Delta \lambda = \lambda_{16 ightarrow 2} - \lambda_{15 ightarrow 2} = \frac{1}{	ext{R}_	ext{H}} \left(\frac{1}{2^2} - \frac{1}{16^2}ight) = \frac{1}{1.097 	imes 10^7 	ext{ m}^{-1}} \left(\frac{1}{4} - \frac{1}{256}ight) = 8.1 	imes 10^{-10} 	ext{ m}$$

What Is the Difference in Wavelength for Spectral Lines Emitted