Question

Which of the following lines in the emission spectrum of hydrogen has the shortest wavelength: red, blue-green, or violet?

Short answer

The violet line in hydrogen's emission spectrum has the shortest wavelength.

Step-by-step solution

Identify the Spectrum of Hydrogen

The hydrogen emission spectrum consists of several series of lines, each corresponding to a transition of an electron between energy levels. The visible lines fall within the Balmer series.

Check the Colors in the Balmer Series

The visible lines in the Balmer series include red, blue-green, and violet, each corresponding to different energy level transitions. Red is for the transition from the third level (n=3 to n=2), blue-green from the fourth level (n=4 to n=2), and violet from the fifth level (n=5 to n=2) or higher.

Determine the Energy Difference

In quantum physics, the larger the energy difference between two levels, the shorter the wavelength. Transitions between higher starting levels (to n=2) involve higher energy than those from lower levels.

Compare Wavelengths Based on Colors

Red has the longest wavelength, followed by blue-green, and violet has the shortest. Therefore, the violet line, corresponding to a transition from either n=5 to n=2 or higher, has the shortest wavelength.

Key concepts

Balmer series

The Balmer series is a significant part of the hydrogen emission spectrum. It's named after Johann Balmer, who discovered a formula to predict the wavelengths of the visible lines for hydrogen.
In the context of the hydrogen atom, the Balmer series involves electron transitions where electrons fall to the second energy level, or shell, known as "n=2".

• These lines are among the few spectral lines that appear in the visible spectrum.
• The series includes transitions from higher energy levels such as n=3, n=4, n=5, and so forth, back down to n=2.
• This drop results in the emission of light across various wavelengths and colors visible to the human eye.

When referring to spectral lines within the Balmer series, you could see red, blue-green, and violet. Each of these colors corresponds to specific electron transitions from higher to lower energy levels, notably the transitions from n=3, n=4, and n=5 to n=2.

Electron transitions

Electron transitions are the key process behind the emission spectra of elements, including hydrogen. When electrons in an atom change energy levels, they either absorb or emit energy.
For the Balmer series:

• Electrons move from a higher energy level down to a lower energy level, specifically ending at n=2.
• Each transition releases a photon of light, and these emitted photons constitute the observable spectrum lines.
• The higher the initial energy level, the more energy is released during the transition.

In hydrogen, when an electron transitions from a higher-level shell such as n=3, n=4, or n=5 and falls to n=2, the energy is released as specific colors of light.
This emitted light creates the visible spectrum of colors we associate with the Balmer series.

Wavelength and energy levels

The relationship between wavelength and energy levels is crucial in understanding the hydrogen emission spectrum. Simply put, the energy difference between two levels directly influences the wavelength of the emitted light.
Here's how it works:

• Larger differences in energy levels result in photons with higher energies and, consequently, shorter wavelengths.
• The formula used to link energy (E) and wavelength (λ) is \(E = \frac{hc}{λ}\) , where \(h\) is Planck’s constant and \(c\) is the speed of light.

In the Balmer series, the violet line, which originates from transitions such as n=5 to n=2, has the shortest wavelength. This is because the electron starts from a higher energy position resulting in a larger energy release when it drops to n=2.
This large energy release manifests as a higher frequency photon, which corresponds to a shorter wavelength, explaining why violet light appears at the shortest end of the visible spectrum.