(a)(1) State the energy transformations which take place during the operation of a modern x-ray tube. (ii) Distinguish between hard and soft x-rays. (iii) S...

Answer Details

(a)(i) Energy transformations in an x-ray tube: electrical energy at the cathode heats the filament (electrical → heat → light), the emitted electrons gain kinetic energy in the accelerating field (electrical → kinetic), and on striking the target this kinetic energy is converted mainly to heat with a small fraction to X-rays (kinetic → heat + X-ray/electromagnetic energy).

(a)(ii) Hard vs soft X-rays: Hard X-rays have very short wavelength, high frequency and high penetrating power (produced by high tube voltage); soft X-rays have longer wavelength, lower frequency and low penetrating power (produced by lower tube voltage).

(a)(iii) Three uses: medical diagnosis (imaging bones/fractures); radiotherapy (treatment of cancer); detection of flaws in metals and inspection of luggage/crystals (crystallography).

(a)(iv) Hazard: over-exposure damages living tissue and can cause cancer or radiation burns. Precautions: shield operators with lead screens/aprons, and limit exposure time / keep a safe distance.

(b) For \(^2_1H + {}^2_1H \to {}^3_1H + {}^1_1H + Q\), the mass defect equals the energy released:

\[ \Delta m = \frac{Q}{931} = \frac{4.03}{931} = 4.33\times10^{-3}\ \text{u}. \]

Mass balance: \((2\times2.01410) - \big[m(^3_1H) + 1.00783\big] = \Delta m\).

\[ 4.02820 - 1.00783 - m(^3_1H) = 4.33\times10^{-3}, \] \[ m(^3_1H) = 3.02037 - 0.00433 = 3.01604\ \text{u}. \]

Atomic mass of \(^3_1H \approx 3.016\ \text{u}\).