Experiment 12 : Moseley's Law

Purpose:

Discussion:

Atomic spectra of all atoms except hydrogen are complex. The transitions involved occur between levels occupied by the outermost electrons which are weakly bound to the nucleus and strongly influenced by other electrons in nearby levels. In contrast, the electrons in the innermost levels of the heavier atoms are most strongly influenced by the highly charged nucleus and are relatively far removed from other electrons. Thus there is a smooth variation, with the charge Z, in the energies of photons produced from transitions between these levels and these spectra, called X-ray spectra, are simple. This fact was first discovered empirically by Henry Moseley in 1913. In this important experiment Moseley directed a beam of energetic electrons onto anodes of various materials in a vacuum and observed the wave- lengths of the resulting radiation. Almost immediately he noticed a close proportionality between the square root of the reciprocal of the wavelength and the atomic number of the anode material. He correctly interpreted this as evidence of the correctness of the recently announced Bohr theory, as it concerns the prediction of the energy levels of electrons in a Coulomb potential. When an incident electron removes one of the two most tightly bound 1s electrons, the electrons in higher shells are attracted to the Z protons in the nucleus, shielded by the spherical distribution of the remaining 1s electron. The effective coulomb charge is thus Z-1 units. The Bohr theory predicts the energy levels should be proportional to the square of this charge so the X-ray energies, which are differences between these levels, are also proportional to (Z-1)².

In this experiment the beam of electrons used by Moseley will be replaced by electrons from a radioactive source, Cs-137. This source emits electrons from beta-decay with an end-point energy of about 0.53 MeV to an excited state which gamma-decays and also emits electrons by internal conversion of about 0.63 MeV. The internal conversion is followed by X-rays from the daughter nucleus, Ba-137. This radiation will be a source of contamination in this experiment. The target materials will be placed near the Cesium source, electrons from this source will remove electrons from the inner shells in the target and the resulting X-rays will be detected by a sodium iodide detector.

Moseley used a crystal spectrometer to analyze the resulting X-rays. This type of spectrometer has excellent energy resolution but is large, difficult to use, and slow. The sodium iodide counter has credible energy resolution and, together with a multi-channel analyzer, provides X-ray spectra in a short running time. It is more efficient for detecting low energy X-rays than higher energy gamma rays but is still subject to the problem of swamping of the spectrum by these intense high energy gamma rays.

Procedure:

Arrange the source, target material and detector so that the total count rate is no more that 1000 counts per second. Support the source so that the target material may be laid on the electron- emitting side of the source and away from the detector. Take runs with as many different target materials as are available. At least use foils of iron, copper, cadmium and tantalum. For each material take a five minute data run. Then carefully remove the material so as not to move the source and take an equal time background run with the analyzer in the subtract mode. The results will be just those events due to the targets. Record the positions of all peaks in the final spectra. Take another spectrum of the source by itself and record the position of the barium X-ray peak. If other sources are available with internally converted gamma rays, take spectra of the resulting X-rays also for these sources.

Report:

For each of the peaks observed plot its peak position versus (Z-1)². It should be possible to find a straight line through the origin that passes through at least one point from each spectrum. Perhaps more than one such line can be determined. Use the position of the barium X-ray (and others if available) to establish an energy scale for the vertical axis. Compare the slope of the steepest line with the theoretical value of 10.2 eV. If other lines can be determined, compare them with what is expected for L X-rays.