(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...
Question 1 Report
(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) State three uses of x-rays.
(iv) Mention one hazard of over-exposure to x-rays in a radiological laboratory, and indicate any two safety precautions.
(b) A possible fusion reaction is \(^2_1 H + ^2_1 H \to ^3_1H + ^1_1H + Q\)
where Q is the energy released as a result of the reaction. If Q = 4.03 MeV, calculate the atomic mass of \(^3_1H\) in atomic mass units. (\(^2_1 H = 2.01410 U; ^1_1H = 1.00783 U; 1U = 931 MeV\))
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 \(^3_1H \approx 3.016\ \text{u}\).
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