Quantum_II_Notes

 2013 Yeow Kok Han Page 1 21 2 eam v eV ---- (Eq 1.1) QQuuaannttuumm PPhhyyssiiccss IIII 11 XX--rraayy SSppeeccttrraa SSeett--uupp The key parts of the x-ray tube are shown in Fig. 1.1 . The heated cathode emits electrons which are accelerated by a high voltage of tens to hundreds of kV. A small portion (1%) of the electrons’ kinetic energies is converted to x-rays when they collide with the tungsten atoms. T he bulk of the kinetic energies become heat that is conducted away by a good conductor or with the use of circulating cooling liquid. An electron reaching t he tungsten target gained KE at the expense of electric PE lost, where Va is the accelerating p.d, me and e are the electron mass and charge respectively. A typical x -ray spectrum can be seen in Fig. 1.2. It is actually a superposition of a continuous spectrum and a line spectrum . These are produced by two different mechanisms at the atomic level. The spikes from the line spectrum occur at two specific wavelengths that are characteristic of the material used as the target. MMeecchhaanniissmm 11 -- AAcccceelleerraattiioonn ooff CChhaarrggee The high speed s of the electrons allow them to penetrate the target atoms. The size of an atom is  10-10 m while the size of a nucleus is  10-15 m and the electron is even smaller. If the nucleus were 1 mm in size, then the atom would be about 100 m across . However, in the vast empty space inside the atom, the elect ric field of the nucleus attracts an incoming electron and curves it around. The strong force and therefore acceleration(centripetal plus linear) results in radiation of an energetic x-ray photon , slowing down the electron in the process. Charged particles are accelerated to high speeds before colliding with target atoms to produce x- rays. The KE gained ½ mv2 = eVa for electrons of charge e. The resulting x- ray spectrum is made up of two parts - a continuous spectrum and a discrete spectrum. The mechanism for the production of continuous spectrum is based on the fact that accelerated or decelerated charges radiate electromagnetic energy. Whenever a charge particle is accelerated or decelerated, it radiates electromagnetic energy. Also, greater acceleration leads to greater rate of radiation. High voltage  10 kV to 200 kV cathode tungsten anode + - copper to conduct heat away electron beam X-rays vacuum glass tube Fig. 1.1 K  relative intensity Fig. 1.2 electron nucleus X-ray photon Fig. 1.3

 2013 Yeow Kok Han Page 2 The x-rays produced in this way are called ‘Brehmsstrahlung’ in German for ‘braking radiation’. Each incoming electron can potentially produce a few such x-ray photons of different energies by interacting with a series of different atoms. Also, an incoming electron can approach nuclei with different proximity and thu