CHAPTER 32 PARTICLE PHYSICS H QUESTIONS AND ANSWERS
Mass of uranium = 3.951 643 × 10−25 kg Mass of radium = 3.753 152 × 10−25 kg Mass of radon 222 = 3.686 602 × 10−25 kg Mass of alpha = 6.646 322 × 10−27 kg Mass of uranium 238 = 238.050 786 u
1.
Thorium 234 = 234.043 600 u Alpha = 4.002 600 u u = 1.66 × 10−27 kg Charge on e− = 1.6 × 10−19 C Speed of light = 3 × 108 m s−1
If 226 88 Ra decays to 222 86 Rn, with the release of an alpha particle, calculate the kinetic energy allocated to
the Rn and the alpha particle, assuming all excess energy is converted to kinetic energy. Solution
Mass of radium – (mass of radon + alpha particle) = decrease in mass 3.753 152 × 10−25 – (3.686 602 × 10−25 + 6.646 322 × 10−27) = 8.678 × 10−30 kg E = mc2 ⇒ E = (8.678 × 10−30)(3 × 108)2 = 7.8102 × 10−13 J
Momentum must be conserved. Ek is divided in inverse proportion to mass. (Add the mass numbers and divide the total energy by the parts. Then allocate inversely.) Mass no. = 222 + 4 = 226
∴ energy per part = 7.8102 × 10−13
__________________ 226
= 3.4558 × 10−15 J (energy in 1 part)
Rn receives 4 of the 226 parts ⇒ 3.4558 × 10−15 × 4 = 1.38234 × 10−14 J Alpha receives 222 of the 226 parts ⇒ 3.4558 × 10−15 × 222 = 7.67197 × 10−13 J
2. 238 92 U disintegrates to 254 90 Th with the release of an alpha particle. Calculate the change in mass and
hence the energy released in the reaction, in joules and eletronvolts.
Solution (Calculate the difference in atomic mass units and then convert to kg)
(ii) E = mc2 ⇒ E = (7.612 76 × 10−30)(3 × 108)2 ⇒ E = 6.85 × 10−13 J (iii) 6.85 × 10−13
_______________ 1.6 × 10−19 = 4.28 MeV
You may now complete Exercise 32A (page 378). First transmutation by artificially
accelerated particles Ernest Rutherford performed the first artificial transmutation in 1919. An artificial transmutation occurs when one element is deliberately converted into another element. Rutherford bombarded nitrogen atoms with alpha radiation, to produce oxygen and hydrogen. This experiment produced the following equation:
