Physics 4e03 Mt2 2002

Physics 4E03 Test 2 March 20, 2002

(1) Above the energy gap corresponding to the magic number 28, the shell model states are

2 p3 2 , 1 f 5 2 , 2 p1 2 , 1g 9 2 , 1g 7 2 , 2d 5 2 , 2d 3 2 , 3s1 2 , and 1h11 2 (in increasing order of energy). 50 and 82 are also magic. Predict the I π values for the ground state and first excited state in

131 49

In and

131 50

Sn .

(2) Interpret the following nuclear spectra of

180 72

Hf :

E(kev) 0

Iπ 0+

93.3

2+

309.3

4+

641.7

6+

Is it a rotating nucleus or a vibrating nucleus? If it is a rotating body, calculate its moment of inertia. If it is a vibrator, what is the energy of the phonon?

(3)

14

C beta decays with a half life of 5730 years.

(a) Complete the symbolic expression associated with the decay process: 14 6

C → 147N + ?

(b) While they are living, organic bodies continuously take in both their ratio of 14

14

C to

12

12

C and

14

C , so

C is about constant, 1.3 × 10 . After a body dies, no more

C is taken in, and the

-12

14

C present at death continuously decreases from

radioactive decay. By measuring the decay rate per gram of a substance, we can calculate when it died. If the measured beta decay rate for 150 g of carbon from a skeleton is 500 decay/minute, how long has the skeleton been dead?

(4) In the decay

Th →

228 90

Ra + α , the highest energy α particle has an energy 5.423

224 88

Mev and the next highest energy is 5.341 Mev. 224

(a) The highest energy decay populates the

Ra ground state. Why is it natural to expect

this to be so? (b) Compute the

Q values for the decay from the measured α energies.

(c) Compute the energy of the first excited state of

224

Ra .

(5) (a) What is the first condition for having α , (b) Calculate the

β −, β +

decay and electron capture.

Q -value in Mev for each of the following nuclear change: 18 9

F → 188O

20 9

( β + decay)

F → 1020Ne ( β − decay)

symbol n 1 H 4 He 14 C 14 N 228 Th 224 Ra 20 F 18 F 18 O 20 Ne

Atomic mass Z 0 1 2 6 7 90 88 9 9 8 10

Constants: Electron mass = me = 5.485803 × 10–4 u = 0.511 Mev/c2 NA = 6.022045 × 1023 mole–1 1 u = 1.660566 × 10–27 kg = 931.502 Mev/c2 1 = = 6.58217 × 10–16 ev.s END

Mass (u) 1.00866501 1.007825 4.002603 14.003242 14.003074 228.028715 224.020186 19.999981 18.000937 17.999160 19.992436