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Chapter 34: Problem 9

Why are the lines of the Lyman series in the ultraviolet while some Balmer lines are in the visible?

Short Answer

Expert verified
The lines of the Lyman series are in the ultraviolet region because they correspond to transitions where the electron falls from a higher energy level to the n=1 level, which releases a high amount of energy and correlates to lower wavelengths (in the ultraviolet region). Whereas some Balmer lines are in the visible region because they correspond to transitions where the electron falls from a higher energy level to n=2, releasing a lower amount of energy that correlates with higher wavelengths (in the visible light spectrum).

Step by step solution

01

The Lyman Series Explanation

The Lyman series of lines in the hydrogen atom corresponds to electronic transitions where the electron falls from a higher energy level to the lowest energy level (n=1). These transitions release a high amount of energy, which corresponds to the ultraviolet region of the light spectrum. According to the energy difference and Planck’s law which states that the energy of a photon is inversely proportional to its wavelength (\(E = \frac{hc}{\lambda}\)), transitions with higher energy correspond to lower wavelength, placing it in the ultraviolet region.
02

The Balmer Series Explanation

The Balmer series, on the other hand, represents transitions where the electron falls from a higher energy level to the second energy level (n=2). These transitions result in the release of a lower amount of energy compared to the Lyman series. According to Planck’s law (\(E = \frac{hc}{\lambda}\)), transitions that release a lower amount of energy correspond to higher wavelengths. Therefore, some of these lines fall in the visible light spectrum, resulting in the characteristic colors we associate with the Balmer series.

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