Topic 13.2 Nuclear Physics. 5 hours. Estimating the Radii of Nuclei. Consider an α-particle that is on a direct collision course with a gold nucleus and its subsequent path. Since the gold nucleus is much more massive than the α-particle we can ignore any recoil of the gold nucleus.
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where the nucleus with atomic number Z has a charge of Ze and the a-particle has a charge of 2e.
For a gold nucleus (Z = 79) and an α-particle with kinetic energy 4.0 MeV we have that
Positive ions of the element under study are produced in a high voltage discharge tube (not shown) and pass through a slit (S1) in the cathode of the discharge tube. The beam of ions is further collimated by passing through slit S2 which provides an entry to the spectrometer. In the region X, the ions move in crossed electric and magnetic fields.
The electric field is produced by the plates P1and P2and the magnetic field by a coil arrangement. The region X acts as a velocity selector. If the magnitude of the electric field strength in this region is E and that of the magnetic field strength is B (and the magnitude of the charge on an ion is e) only those ions which have a v velocity given the expression Ee = Bev will pass through the slit S3 and so enter the main body, Y, of the instrument.
A uniform magnetic field, B´, exists in region Y and in such a direction as to make the ions describe circular orbits. For a particular ion the radius r of the orbit is given by,
Since all the ions have very nearly the same velocity, ions of different masses will describe orbits of different radii, the variations in value depending only on the mass of the ion.
A number of lines will therefore be obtained on the photographic plate P, each line corresponding to a different isotopic mass of the element. The position of a line on the plate will enable r to be determined and as B´, e and v are known, m can be determined.
IB Outcome 13.2.2
- Students should be able to draw a schematic diagram of the Bainbridge mass spectrometer, but the experimental details are not required.
- Students should appreciate that nuclear mass values provide evidence for the existence of isotopes.
where λ is the constant of proportionality called the decay constant and is defined as ‘the probability of decay of a nucleus per unit time’ and has units of s-1.
NOTE: 1 Bq (Becquerel) = 1 decay / second
an outline of the methods
available for measuring half-
lives and are sufficient for the
actual measurement can be very tricky. For example, many radioactive isotopes decay into isotopes that themselves are radioactive and these in turn decay into other radioactive isotopes. So, although one may start with a sample that contains only one radioactive isotope, some time later the sample could contain several radioactive isotopes.
Tsokos, Page 412
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