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Chapter 8: Problem 18

A line is detected in the hydrogen spectrum at \(1880 \mathrm{nm}\). Is this line in the Balmer series? Explain.

Short Answer

Expert verified
The answer requires calculation of \( n \) using the Balmer series formula, and then checking if it is an integer greater than 2 for it to belong to the Balmer series. The exact answer can only be determined after the calculation.

Step by step solution

01

Convert wavelength to meters

To utilize the formula of Balmer series, the given wavelength must be in meters. Convert \(1880 \, \mathrm{nm}\) to meters. 1 \, \mathrm{nm} = \(1 \times 10^{-9} \, \mathrm{m}\). Therefore, \(1880 \, \mathrm{nm} = 1880 \times 10^{-9} \, \mathrm{m} = 1.88 \times 10^{-6} \, \mathrm{m}\).
02

Apply the Formula of Balmer Series

Substitute \( \lambda = 1.88 \times 10^{-6} \, \mathrm{m} \) in the Balmer formula to solve for \( n \). Thus, calculate \( n \) by solving \( 1/(1.88 \times 10^{-6}) = 1.097373 \times 10^7 (1/4 - 1/n^2) \) for \( n \).
03

Check if n is an integer

Solve for \( n \) and check if it is an integer value. Balmer series corresponds to transitions where the electron falls to the 2nd energy level from higher levels. The value of \( n \) must be an integer higher than 2 for the wavelength to be in the Balmer series. If it is not an integer or it is less than or equals to 2, the wavelength is not in the Balmer series.

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Most popular questions from this chapter

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