## Problem 1.57

$c=\lambda v$

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### Problem 1.57

Problem 57 from Chapter 1 in the textbook:

Lines in the Balmer series of the hydrogen spectrum are observed at 656.3, 486.1, 434.0, and 410.2 m. What is the wavelength of the next line in the series?

How do you start off/solve this problem?

Kyle Sheu 1C
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Joined: Fri Jun 23, 2017 11:39 am

### Re: Problem 1.57

This question requires that you have some knowledge of spectral lines. The Balmer series, in the visible region, has lines where n1=2 (for the record, the Lyman series (UV region) has lines where n1=1 and the Paschen series (infrared region) has lines where n1=3).

The problem gives us 4 lines, so we know that lines corresponding to n2=3 through n2=6 have been accounted for. The next line would thus have n2=7. From there, you can use the Rydberg formula (found on p. 7) to determine frequency, and use c=λν to solve for wavelength!

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As a second option, you can also use En=-hR/n2, where n=2 and n=7 to determine the energy drop between these two levels. Use E=hv to determine v, and use c=λν to determine wavelength.

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