Introduction to Moseley’s Law
Soon after Rutherford’s scattering theory had been confirmed by experiment (about 1913), the one-to-one association of an atomic number Z with each element was solidified by the work of Henry Moseley (1887- 1915). He used Bohr’s model of atomic structure to determine the energy emitted when low-level electrons change orbitals. This energy has a strong dependence on an atomic number so that by measuring the energy of the x-rays characteristic of an element, its atomic number Z can be unambiguously determined. In today’s lab, you will measure the x-ray spectra of a number of elements and also identify several unknown elements by looking at their characteristic x-ray spectra.
Moseley’s law is an empirical law concerning the characteristic x-rays that are emitted by atoms. The law was discovered and published by the English physicist Henry Moseley in 1913.
A widespread simplification is an idea that the effective charge of the nucleus decreases by 1 when it is being screened by an unpaired electron that remains behind in the K-shell. In any case, Bohr’s formula for Moseley’s K-alpha X-ray transitions became:
- The setup is quite simple. First, a 57Co γ-ray source decays in such a way as to produce (among other things) several photons mainly consisting of 136 keV, 122 keV, and 14 keV γ-rays. [Later in the course we will learn that the 57Co undergoes electron capture, the product of which is a 57Fe nucleus in an excited state. Upon relaxation the 57Fe nucleus emits the γ−rays.] The γ-rays strike the shielded target and knock electrons out from the target atoms. Other electrons drop to fill the hole created by the ejected electron and in the process emit characteristic x-rays.
- A proportional tube is used to detect the x-rays. It consists of a chamber filled with a noble gas (typically xenon). A thin positively charged wire runs along the axis. When an x-ray interacts inside the tube, it ejects electrons from the gas atoms. These are attracted to the wire, speed up enough to eject other electrons, and eventually cause a cascade of electrons to accelerate toward the wire. This charge pulse is amplified and recorded. The strength of the signal is proportional to the x-ray energy deposited in the tube; hence the name “proportional tube.” Please be very careful with the tube because the Be window is very thin and fragile.
- You will use a multi-channel analyzer to determine x-ray energies. The multi-channel analyzer is mounted on a card inside the PC. A multi-channel analyzer measures all the voltage pulses from the proportional tube and sorts them into bins according to their strength. Each bin records pulses that fall within a set energy range and the bins form a sequential array so that the bin number N is proportional to the strength of the voltage pulse (which, if we use a proportional tube, is proportional to the x-ray energy.)
- The detector will see more than just the x-rays of interest to you. In addition, γ-rays directly from the Co source will strike the detector. More importantly, source γ’s will also interact in the shielding, producing a lead x-ray spectrum. Since there is so much more the lead shielding than there is a sample, this may mask the signal. To eliminate this background, the data are accumulated in two steps. First, with the multi-channel analyzer on add, data are accumulated for some predetermined time. Then the sample is removed and the analyzer is set to subtract. Data are accumulated for the same amount of time. This eliminates the background counts at the same rate they were accumulated, resulting in data which represent only the contribution from the sample.
- First measure the x-ray spectra of six known samples: Al, Ti, Cu, Zr, Ag, and Te. Save your data to files that you can read later.
- Measure the spectra from two of unknown elements. Again, save your data to files that you can read later.
- First, you should confirm Moseley’s law with six known samples. Since the energy of the characteristic x-ray should (according to Moseley) be proportional to (Z-δ) 2 and channel number N is proportional to E, then N is proportional to (Z-δ) 2. Thus, N kZ = − bg δ. Make a plot of N vs. Z for the six known samples. Obtain the best value of k and δ from this graph. Look at your spectra carefully and think about what the uncertainties in your data are. Devise a reasonable method for determining the uncertainties in δ and k.
- Determine Z for the unknowns by comparing the peak position for each with your results from the six known samples. Don’t forget about the uncertainty associated with this determination.