Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁  4 to n₂  8 transition. A)1,947 nm B)1,632 nm C)1,058 nm D)725 nm E)421 nm

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Quizplus · Accepted Answer

The wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 4 to n₂ F1F1F1S1F1F1F10 8 transition can be calculated using the Rydberg formula:$$\frac{1}{\lambda}=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$$where R_H is the Rydberg constant for hydrogen (1.0973731×10^7 m^-1).Substituting the given values into the formula, we get:$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{1}{4^2}-\frac{1}{8^2})$$$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{1}{16}-\frac{1}{64})$$$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{3}{64})$$$$\frac{1}{\lambda}=5.167548 imes10^6 m^{-1}$$$$\lambda=\frac{1}{5.167548 imes10^6 m^{-1}}=1.936 imes10^{-6} m=1,936 nm$$Therefore, the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 4 to n₂ F1F1F1S1F1F1F10 8 transition is 1,936 nm, which is closest to choice A) 1,947 nm.

Determine the Wavelength of the Line in the Hydrogen Atom