(iv) hazards of x-rays.
(b) The potential difference between the cathode and target of an x-ray tube is 5.00 x 10\(^4\)V and the current in the tube is 2.00 x 10\(^{-2}\)A. Given that only one percent of the total energy supplied is emitted as x-radiation, determine the ospheric pressure.
(ii) rate at which heat is removed from the target in order to keep it at steady temperature. [Planck's constant, h = 6.63 x 10\(^{-34}\) Js, electronic charge e = 1.60 x 10\(^{-19}\) C]
(a)(i) Two properties of X-rays: they travel in straight lines at the speed of light and are not deflected by electric or magnetic fields (uncharged); they penetrate matter and affect photographic plates.
(ii) Two reasons showing X-rays are waves: they undergo diffraction (and interference) when passed through crystals; they travel with the speed of light and are part of the electromagnetic spectrum (they are not deflected by fields).
(iii) Two uses of X-rays other than in medicine: detecting flaws/cracks in metal castings and welds (industrial radiography); studying crystal structure by X-ray diffraction (crystallography); security screening of luggage.
(iv) Two hazards of X-rays: they damage/destroy living body cells and tissues; prolonged exposure can cause burns, cancer or genetic mutation.
(b) \(V = 5.00 \times 10^{4}\ \text{V}\), \(I = 2.00 \times 10^{-2}\ \text{A}\).
(i) Maximum frequency: the fastest electrons give up all their energy \(eV\) to a single photon, so \(hf_{max} = eV\):
\[ f_{max} = \frac{eV}{h} = \frac{1.60 \times 10^{-19} \times 5.00 \times 10^{4}}{6.63 \times 10^{-34}} \]
\[ f_{max} = \frac{8.0 \times 10^{-15}}{6.63 \times 10^{-34}} = 1.21 \times 10^{19}\ \text{Hz} \]
(ii) Rate of heat removal: total power supplied is:
\[ P = VI = 5.00 \times 10^{4} \times 2.00 \times 10^{-2} = 1000\ \text{W} \]
Only 1% becomes X-radiation, so 99% appears as heat that must be removed:
\[ P_{heat} = 0.99 \times 1000 = 990\ \text{W} \]
Heat is removed at the rate of \(990\ \text{J s}^{-1}\) (990 W).
