Structure of Matter · Atomic models and periodicity
Spectra and the Bohr model
Pass white light through a prism and you get a continuous rainbow with no gaps. Now do the same with the light from a hydrogen discharge tube and you see only a few coloured lines, separated by darkness. Classical physics could not explain this pattern. It was the first serious clue that the energy of an electron in an atom cannot take just any value.
Continuous and line spectra
Flame tests and line spectra are used to identify elements. Each metal ion gives a characteristic flame colour: lithium crimson red, sodium yellow (a strong line at 589 nm), potassium lilac, copper blue-green, barium apple green and strontium red. The line spectra of sodium, strontium and copper are different "fingerprints".
To identify an element from its line spectrum, compare the positions of the lines with those of known elements. For example, an unknown sample gives a flame test that is yellow, and its emission spectrum has a strong line at about 589 nm. Sodium has exactly this line, so the sample contains sodium. A red flame whose spectrum has several lines in the red and orange regions would point to strontium instead. A blue-green flame points to copper.
The table gives approximate secondary data for the strongest visible lines. Compare an unknown spectrum with these values.
Element
Flame colour
Strong visible lines (nm, approximate)
Sodium
yellow
589
Strontium
red
461 (blue), 606 to 680 (orange and red)
Copper
blue-green
510 to 580 (green region)
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The analysis of light emitted or absorbed by substances is a fundamental tool for understanding the electron shell of the atom. a) Explain the essential physical…
The analysis of light emitted or absorbed by substances is a fundamental tool for understanding the electron shell of the atom.
a) Explain the essential physical difference between a continuous spectrum and a discontinuous or line spectrum.
b) Justify why the atomic emission spectrum of a low-pressure gas consists of discrete lines, and explain how these lines correspond to those observed in its absorption spectrum.
According to classical physics, an accelerating charge radiates energy continuously, so an orbiting electron should spiral into the nucleus in about $10^{-11}\ \text{s}$. Yet atoms are stable. Why do electrons not fall into the nucleus?
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In the atomic model proposed by Bohr for the hydrogen atom, the energy associated with each electronic level depends on the principal quantum number $n$ through the…
In the atomic model proposed by Bohr for the hydrogen atom, the energy associated with each electronic level depends on the principal quantum number $n$ through the expression:
Heat sodium vapour in a flame and it gives out a very pure yellow light of wavelength 589.0 nm. Cool sodium vapour lit by white light absorbs exactly that same wavelength, leaving a dark line in the spectrum. What happens inside the atom to make an element emit and absorb photons of identical energy?
Spectral series
Transitions that end on the same level form a series. The Lyman series ends on $n_f = 1$ and lies in the ultraviolet. The Balmer series ends on $n_f = 2$ and lies mainly in the visible region.
To find the starting level $n_i$ from a measured wavelength, first get the photon energy from $E = hc/\lambda$, then solve $E = 2.18 \times 10^{-18}\left(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2}\right)$ for $n_i$.
The diagram below gives the energies of the first levels of hydrogen, so you can use $E_m - E_n = hf$ directly with given values.
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The following diagram shows the first three energy levels of the hydrogen atom and two electronic transitions labelled A and B: . Using the diagram and the data…
The following diagram shows the first three energy levels of the hydrogen atom and two electronic transitions labelled A and B:
. Using the diagram and the data provided:
a) Explain whether transitions A and B correspond to processes of energy absorption or emission.
b) Calculate the energy (in $\mathrm{eV}$) and the wavelength (in $\mathrm{nm}$) of the photon involved in transition A ($3 \rightarrow 2$), and state, with reasoning, which of the two transitions (A or B) emits radiation of shorter wavelength.
Ionisation energy and limitations of the Bohr model
Limitations of the model
The Bohr model explains the hydrogen line spectrum very well, but it has important limitations:
It works only for hydrogen and other one-electron species such as $\text{He}^+$. In those cases $E_n = -2.18 \times 10^{-18}\,Z^2/n^2\ \text{J}$. For atoms with more than one electron, the repulsion between electrons is ignored and the model fails.
It cannot explain the fine structure of spectra: at high resolution, each line splits into several closer lines.
It gives the electron a fixed circular orbit at a definite distance from the nucleus. Real electrons are better described by the orbital model, which you will meet next. It replaces orbits with orbitals: regions of high probability of finding the electron.
Back to the start: The hydrogen tube gives only a few visible lines because its electrons fall from higher levels ($n = 3, 4, 5, 6$) to $n = 2$ (the Balmer series). Each coloured line is a photon of energy exactly $|E_2 - E_n|$ for one transition.
Summary
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