07 2.3 The hydrogen spectrum explained
- When the excited electron falls to the second level (n = 2) from n = 3, 4, 5, 6, the energy released is visible light: n = 3→2 gives the red line (656 nm); 4→2 gives the green (486 nm); 5→2 blue (434 nm); 6→2 violet (410 nm). These make up the visible line spectrum of hydrogen.
- When the electron returns to the first level (n = 1), the energy released is greater and the lines are in the ultraviolet region, invisible to the eye.
- Transitions to levels n = 3 and higher give lines in the infrared region, also invisible.
Important observations of Bohr's calculations:
- The energy differences between neighbouring levels are not equal; they decrease as we move away from the nucleus. Hence the quantum needed to move an electron between different levels is not constant, and each transition gives a different line.
- The electron never stays between levels; it moves in definite jumps from one level to another.
- The larger the energy gap, the shorter the wavelength (higher frequency) of the emitted light, so 6→2 (violet) has a larger gap than 3→2 (red).
Worked example 2.1. Which transition of hydrogen gives the line of the greatest energy among the four visible lines? The violet line, 410 nm (the shortest wavelength), arising from the electron falling from n = 6 to n = 2. The red line (3→2, 656 nm) has the smallest energy.
✍️ Worked examples
Worked example 2.2.
- Explain why the electron in a hydrogen atom, heated strongly, gives several lines even though there is only one electron.
- Because a large number of atoms are present in the sample; different atoms have their electrons excited to different levels and fall back by different routes, so all the possible transitions are emitted simultaneously.
Worked example 2.3. The electron of hydrogen is raised from n = 1 to n = 3 and falls directly back to n = 1. What type of radiation is emitted? Ultraviolet, since the end level is n = 1.