# Chapter 13: Nuclei

13.1 (a) Two stable isotopes of lithium 6 3 Li and 7 3 Li have respective

abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes, 10 5B and 11 5B. Their respective

masses are 10.01294 u and 11.00931 u, and the atomic mass of

boron is 10.811 u. Find the abundances of 10 5B and 11 5 B.

**Answer:**

**a).**

**b).**

13.2 The three stable isotopes of neon: 20 21 22

10 10 Ne, Ne and Ne 10 have

respective abundances of 90.51%, 0.27% and 9.22%. The atomic

masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u,

respectively. Obtain the average atomic mass of neon.

13.3 Obtain the binding energy (in MeV) of a nitrogen nucleus ( ) 14 7 N , given m ( ) 14 7 N =14.00307 u

13.4 Obtain the binding energy of the nuclei 56 26Fe and 209 83 Bi in units of MeV from the following data: m (56 26Fe ) = 55.934939 u m ( 209 83 Bi ) = 208.980388 u

13.5 A given coin has a mass of 3.0 g. Calculate the nuclear energy that

would be required to separate all the neutrons and protons from

each other. For simplicity assume that the coin is entirely made of

63

29Cu atoms (of mass 62.92960 u).

13.6 Write nuclear reaction equations for

(i) α-decay of 226 88 Ra (ii) α-decay of 242 94 Pu (iii) β– -decay of 32 15 P (iv) β– -decay of 210 83 Bi (v) β+ -decay of 11 6 C (vi) β + -decay of 97 43 Tc (vii) Electron capture of 120 54 Xe

13.7 A radioactive isotope has a half-life of T years. How long will it take

the activity to reduce to a) 3.125%, b) 1% of its original value?

13.8 The normal activity of living carbon-containing matter is found to

be about 15 decays per minute for every gram of carbon. This activity

arises from the small proportion of radioactive 14 6 C present with the stable carbon isotope 12 6 C . When the organism is dead, its interaction

with the atmosphere (which maintains the above equilibrium activity)

ceases and its activity begins to drop. From the known half-life (5730

years) of 146 C , and the measured activity, the age of the specimen

can be approximately estimated. This is the principle of 14

6C dating used in archaeology. Suppose a specimen from Mohenjodaro gives

an activity of 9 decays per minute per gram of carbon. Estimate the

approximate age of the Indus-Valley civilisation.

13.9 Obtain the amount of 60 27Co necessary to provide a radioactive source of 8.0 mCi strength. The half-life of 60 27Co is 5.3 years.

13.10 The half-life of 90 38Sr is 28 years. What is the disintegration rate of

15 mg of this isotope?

13.11 Obtain approximately the ratio of the nuclear radii of the gold isotope

197 79 Au and the silver isotope 107 47 Ag .

13.12 Find the Q-value and the kinetic energy of the emitted α-particle in

the α-decay of (a) 226 88 Ra and (b) 220 86 Rn . Given m ( 226 88 Ra ) = 226.02540 u, m ( 222 86 Rn ) = 222.01750 u, m ( 220 86 Rn ) = 220.01137 u, m ( 21 84 Po ) = 216.00189 u.

Kinetic energy of α-particle ≈Q\approx Q≈Q.

13.13 The radionuclide 11C decays according to

11 11 + 6 5 1/2 C B+ + : =20.3 min → e T ν

The maximum energy of the emitted positron is 0.960 MeV.

Given the mass values:

m (11 6 C) = 11.011434 u and m (11 6B ) = 11.009305 u,

calculate Q and compare it with the maximum energy of the positron

emitted.

**Answer:**

13.14 The nucleus 23 10 Ne decays by β– emission. Write down the β-decay equation and determine the maximum kinetic energy of the

electrons emitted. Given that:

m (23 10 Ne ) = 22.994466 u m (23 11 Na ) = 22.989770 u.

**Answer:**

**Answer:**

13.16 Suppose, we think of fission of a 56 26Fe nucleus into two equal fragments, 28 13 Al . Is the fission energetically possible? Argue by working out Q of the process. Given m ( 56 26Fe ) = 55.93494 u and m ( 28 13 Al ) = 27.98191 u.

**Answer:**

13.17 The fission properties of 239 94 Pu are very similar to those of 235 92 U . The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure 239 94 Pu undergo fission?

**Answer:**

13.18 A 1000 MW fission reactor consumes half of its fuel in 5.00 y. How

much 235 92 U did it contain initially? Assume that the reactor operates

80% of the time, that all the energy generated arises from the fission

of 235v92 U and that this nuclide is consumed only by the fission process.

**Answer:**

13.19 How long can an electric lamp of 100W be kept glowing by fusion of

2.0 kg of deuterium? Take the fusion reaction as

2 2 3

1 1 2 H+ H He+n+3.27 MeV →

Answer:

13.20 Calculate the height of the potential barrier for a head on collision

of two deuterons. (Hint: The height of the potential barrier is given

by the Coulomb repulsion between the two deuterons when they

just touch each other. Assume that they can be taken as hard

spheres of radius 2.0 fm.)

Answer:

13.21 From the relation R = R0A 1/3, where R0 is a constant and A is the

mass number of a nucleus, show that the nuclear matter density is

nearly constant (i.e. independent of A).

Answer:

13.22 For the β+(positron) emission from a nucleus, there is another

competing process known as electron capture (electron from an inner

orbit, say, the K–shell, is captured by the nucleus and a neutrino is

emitted).

Answer:

Show that if β + emission is energetically allowed, electron capture is necessarily allowed but not vice–versa.

Answer:

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