(a) Explain the following terms:
(i) mass defect;
(ii) binding energy of a nucleus.
(b)(i) Assuming the wave nature of an electron, what is the effect of decreasing the speed of a photoelectron on its; ((alpha)) wavelength? ((beta)) energy?
(ii) A particle of friasS 4.4 x 10(^{-23}) kg moves with a velocity of 10(^5)ms(^{-1}). Calculate its wavelength. (h = 6.6 x 10(^{-34}) Js)
The diagram above shows part of a radioactive decay series. Use it to answer the following questions.
(i) Name a pair of isotopes.
(ii) Name the isotopes with which the series starts.
(iii) Write down a nuclear equation for two ekgmples of each of: ((alpha)) alpha decay; ((beta)) beta decay.
Explanation
(a)(i) Mass defect is the difference between the mass of a nucleus and the total mass of its nucleons. It expressed in atomic mass unit (a.m.u.). It is also a measure of binding energy.
Mass defect = total mass of nucleus
– mass of nucleons.
(ii) Binding energy is the work done or energy needed to separate the nucleons in a nucleus. It is measured in eV or Joules (J).
(b)(i) The effect of decreasing the speed of a photoelectron on: ((alpha)) wavelength –> wavelength increases. ((beta)) energy —> energy decreases.
(ii) (lambda = frac{h}{mv})
= (frac{6.6 times 10^{-34}}{4.4 times 10^{-2} times 10^{-16}})m
(c) Pairs of isotopes in the figure are;
(^{208}_{82}Pb) and (^{212}_{82}Pb) or (^{212}_{84}Po) and (^{216}_{84}Po) or
(^{224}_{88}Ra) and (^{288}_{88}Ra) or (^{288}_{90}Th) and (^{232}_{90}Th)
(ii) The series started with isotopes (^{232}_{90}Th)
(iii) Nuclear equation for;
(alpha)Alpha decay
(^{232}_{90}Th) (to) (^{228}_{88}Ra) + (^{4}_{2}He) + Energy;
(^{228}_{90}Th) (to) (^{22}_{88}Ra) + (^{4}_{2}He) + Energy;
(^{224}_{88}Ra) (to) (^{220}_{86}Rn) + (^{4}_{2}He) + Energy;
(^{212}_{84}Po) (to) (^{208}_{82}Pb) + (^{4}_{2}He) + Energy;
(^{216}_{84}Po) (to) (^{212}_{82}Pb) + (^{4}_{2}He) + Energy;
(^{212}_{84}Rn) (to) (^{208}_{82}Po) + (^{4}_{2}He) + Energy;
(^{220}_{84}Rn) (to) (^{216}_{84}Po) + (^{4}_{2}He) + Energy;
(^{216}_{84}Rn) (to) (^{212}_{82}Pb) + (^{4}_{2}He) + Energy;
((beta)) Beta decay
(^{224}_{88}Ra) (to) (^{224}_{89}Ac) + (^{o}_{-1}e) + Energy;
(^{228}_{88}Ac) (to) (^{228}_{90}Ac) + (^{o}_{-1}e) + Energy;
(^{212}_{82}Pb) (to) (^{212}_{83}Bi) + (^{o}_{-1}e) + Energy;
(^{212}_{83}Ra) (to) (^{212}_{84}Ac) + (^{o}_{-1}e) + Energy;