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UNIVERSITI TUNKU ABDUL RAHMAN Centre : Centre for Foundation Studies (CFS) Session : 201610 Course : Foundation in Science Unit Code : FHSC 1034 Year : Year 1 Unit Title : Waves and Modern Physics Trimester : Trimester 2 / 3 Tutorial No.10–Nuclear Physics (Part 1) Table below will be useful for many of these problems. A more completelist of atomic masses can be obtained from internet or books . Elemen t Atomic Mass (u) Element Atomic Mass (u) ( e 0 1 - ) 0.000 549 Na 23 11 22.989 770 ( n 0 1 ) 1.008 665 Mg 23 12 22.994 127 H 1 1 1.007 825 Al 27 13 26.981 538 H 2 1 2.014 102 P 30 15 29.978 310 He 4 2 4.002 602 Ca 40 20 39.962 591 Li 7 3 7.016 003 Ca 42 20 41.958 622 Be 9 4 9.012 174 Ca 43 20 42.958 770 B 10 5 10.012 936 Fe 56 26 55.934 940 C 12 6 12.000 000 Zn 64 30 63.929 144 C 13 6 13.003 355 Cu 64 29 63.929 599 N 14 7 14.003 074 Nb 93 41 92.906 377 N 15 7 15.000 108 Au 197 79 196.966 543 O 15 8 15.003 065 Hg 202 80 201.970 617 O 17 8 16.999 131 Po 216 84 216.001 790 O 18 8 17.999 160 Rn 220 86 220.011 401 F 18 9 18.000 937 Th 234 90 234.043 583 Ne 20 10 19.992 435 U 238 92 238.050 784 1. What is the order of magnitude of the number of protons in your body? Of the number of neutrons? Of the number of electrons? (Ans: ~10 28 protons, ~10 28 neutrons, ~10 28 electrons) 2. Consider the hydrogen atom to be a sphere of radius equal to the Bohr radius, 0.53 × 10 −10 m, and calculate the approximate value of the ratio of the nuclear density to the atomic density. (Ans: 8.6 × 10 13 )

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3. Singly ionized carbon atoms are accelerated through 1 000 V and passed into a mass spectrometer to determine the isotopes present. The magnetic field strength in the spectrometer is 0.200 T. (a) Determine the orbital radii for the 12 C and the 13 C isotopes as they pass through the field. (b) Show that the ratio of the radii may be written in the form below and verify that your radii in part (a) satisfy this formula. 2 1 2 1 m m r r (Ans: 8.21 cm, 80.961) 4. Calculate the average binding energy per nucleon of Nb 93 41 and Au. 197 79 (Ans: 8.66 MeV/nucleon, 7.92 MeV/nucleon) 5. Two nuclei having the same mass number are known as isobars . Calculate the difference in binding energy per nucleon for the isobars Na 23 11 and Mg. 23 12 How do you account for this difference? ( Ans: 0.210 MeV/nucleon, less proton repulsion in N 11 23 a ) 6. Calculate the binding energy of the last neutron in the Ca 43 20 nucleus. [Hint: You should compare the mass of Ca 43 20 with the mass of Ca 42 20 plus the mass of a neutron. The mass of Ca 42 20 = 41.958 622 u.] (Ans: 7.93 MeV) 7. A drug tagged with Tc 99 43 (half-life = 6.05 h) is prepared for a patient. If the original activity of the sample was 1.1 × 104 Bq, what is its activity after it has sat on the shelf for 2.0 h? (Ans: 8.7 × 10 3 Bq) 8. Radon gas has a half-life of 3.83 days. If 3.00 g of radon gas is present at time t = 0, what mass of radon will remain after 1.50 days have passed? (Ans: 2.29 g) 9. After a plant or animal dies, its 14 C content decreases with a half-life of 5 730 yr. If an archaeologist finds an ancient firepit containing partially consumed firewood, and the 14 C content of the wood is only 12.5% that of an equal carbon sample from a present- day tree, what is the age of the ancient site?

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