Chapter 29:Nuclear Physics

Some Properties of Nuclei

Homework : Read and understand the lecture note.

Some terminology• Atomic number Z : number of protons in the nucleus Neutron number N : number of neutrons in the nucleus Mass number A : number of nucleons (protons and neutrons) in the nucleus• The symbol used to represent the nucleus of an atom is .• An isotope of an element has the same Z value but different N and A values.

XAZ

Charge and mass• Proton charge +e : 1.602 x 10-19 C• Electron charge –e : -1.602 x 10-19 C• Unified mass unit u : the mass of one atom of the isotope 12C = 12 u 1 u =1.660 x 10-27 kg = 931.5 MeV/c2

• Electron mass : 5.486 x 10-4 u = 0.511 MeV/c2

• Proton mass : 1.6726 x 10-27 kg = 1.007 u = 938.3 MeV/c2

• Neutron mass : 1.6750 x 10-27 kg = 1.009 u = 939.6 MeV/c2

Size of nuclei

Some Properties of Nuclei

• How close an particle can approach to a nucleus of charge Ze?

d

Zeek

r

qqkmv ee

))(2(

2

1 212

silverfor fm 20

nucleus goldfor fm 32m 102.34 14

2

2

mv

Zekd e

Rutherford’s estimate1 fm = 10-15 m

Approximately most nuclei are spherical andhave an average radius r : 3/1

0Arr

All nuclei have nearly the same density. Nuclear stability• The force that bind nucleon together (strong force) is stronger than the Coulomb force – this gives stability to nuclei.• Light nuclei are most stable if N=Z, while heavy nuclei are more stable if N>Z.

Binding energy

Binding Energy

• The total mass of a nucleus is always less than the sum of the masses of its nucleons. Therefore the total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons. This difference is called binding energy.• Binding energy of deuteron – a bound system of a neutron and a proton (also the nucleus of deuterium)

MeV 2.224u) MeV)/(1 5.931)(u 002388.0(

u0.002388u 014102.2)u 008665.1u 007825.1()(

b

dnp

E

mmmm

• Binding energy per nucleon peaks at about A=60. This means the elements around this peak are more stable. The average binding energy per nucleon is 8 MeV.

Types of radiation emitted from a radio active substance

Radio Activities

• Alpha () (nucleus of 42He)

• Electron (e-) or positron (e+) (anti-electron)• Gamma ray ( )

Decay constant and half-life• Observations established that if a radioactive sample contains N radioactive nuclei at some instance, the number of nuclei, N, that decay in a short time interval t is proportional to N.

Nt

N

tNN

teNN 0

N decreases

decay constant

• The decay rate or activity R of a sample is defined as the number of decays per second:

Nt

NR

exponential decay

Radio Activities Decay constant and half-life (cont’d)• Exponential decay and half-life

teNN 0 exponential decay

- The half-life T1/2 of a radio active substance is the time it takes for half of a given number of radioactive nuclei to decay.

2/10

2

1

T

tnNN

n

2/10

0

2TeN

N

693.02ln

2/1 T

• Units of activity R (curie and becquerel)

decays/s 103.7Ci 1 10 unit) (SI decay/s 1Bq 1

Radio Activities Example 29.3: Activity of radium• The half-life of the radioactive nucleus is 1.6x103 yr. If a sample contains 3.00x1016 such nuclei, determine the followings: (a) the initial activity in curies

s 105.0s/yr) 10yr)(3.156 106.1( 10732/1 T

-1112/1 s 104.1/693.0 T

(b) the number of radium nuclei remaining after 4.8x103 yr

Ci 11Ci 101.1decays/s 102.4 -5500 NR

Ra22688

lives-half 0.3life-yr/half 106.1

yr 108.43

3

n

nuclei 108.32)nuclei)(1/ 100.3()2/1( 153.0160 NNN n

(c) the activity at this later time

Ci 1.4decays/s 103.5 4 NR

Radio Activities Example 29.4: Radon gas• Radon is a radioactive gas that can be trapped in the basements of homes, and its presence in high concentrations is a known health hazard. radon has a half-life of 3.83 days. A gas sample contains 4.00x108 radon atoms initially. (a) How many atoms will remain after 14.0 days have passed if no more radon leaks in?

Rn22286

-12/1 day 181.0/693.0 T

atoms 1017.3atoms) 1000.4( 7days) 0.14)(day 181.0(80

-1

eeNN t

(b) What is the activity of the radon sample after 14.0 days?-1-64-1 s 102.09s) 10day/8.64 1)(day 181.0(

Bq 66.3decays/s 3.66 NR (c) How much time must pass before 99% of the sample has decayed?

tNeNeNN tt )ln()ln()ln()ln()ln( 000

days 25.5s 1020.2s 1009.2

))01.0/(ln()/ln()ln()ln( 61-60000

NNNNNNt

Decay Processes Alpha decay• If a nucleus emits an alpha particle , it loses two protons and two neutrons. So the reaction can be written symbolically as:

He42

HeYX AZ

AZ

42

42

X : parent nucleus, Y : daughter nucleus

• Two examples:

HeThU 24

23490

23892

HeRnRa 42

22286

22688

half-life : 4.47x109 years

half-life : 1.60x103 years

• For alpha emission to take place, the mass of the parent must be greater than the combined mass of the daughter and the alpha particle. The excess mass is converted to kinetic energy of the daughter nucleus and the alpha particle.

• Since momentum is conserved, two particles in the final state carry the same momentum in the opposite direction if they are produced by the parent nucleus at rest. As the kinetic energy KE=p2/(2m), the heavier particle carries more energy.

Decay Processes Alpha decay (cont’d)• Example 29.5 : Decaying radium

HeRnRa 42

22286

22688

Calculate the amount of energy liberated in the decay:

u 226.020173u 4.002602 u 017571.222 mmdu. 0.005229u 020173.226u 025402.226)( mmMm dp

MeV 4.871MeV/u) u)(931.494 005229.0( E

Decay Processes Beta decay• If a nucleus emits a particle, the daughter nucleus has the same number of nucleons as the parent nucleus but the atomic number is changed by 1. So the reaction can be written symbolically as:

eAZ

AZ eYX

1

• An example:

eeNC 147

146

eAZ

AZ eYX

1

In this case the electron comes from the decay of neutron:

eepn 11

10

• Example 29.6 : Beta decay of carbon-14

MeV 0.156MeV) u)(931.494 000168.0(

u 0.000168u 003074.14u 003242.14

E

mmm NC

Decay Processes Gamma decay• Often a nucleus that undergoes radioactive decay is left in an excited energy state. the nucleus can then undergoes a second decay to a lower energy state by emitting one or more photons (called gamma rays).

• Carbon dating• Smoke detector• Radon detection

eeCB *126

125

C126

Practical uses of radio activity (See the textbook for detains)

Nuclear Reactions Nuclear reactions• The structure of nuclei can be changed by bombarding them with energetic particles. Such changes are called nuclear reactions.• First person who observed a nuclear reaction in the following process was Rutherford. He found that protons were released when alpha particles were allowed to collide with nitrogen atoms:

By balancing atomic numbers and mass numbers, we can conclude that the known nucleus X is in fact isotope of oxygen:

HXNHe 11

147

42

HONHe 11

178

147

42

Example 29.8 : Discovery of neutron by Chadwick (1932)

XCBeHe AZ 12

694

42Reaction used:

0642

11294

ZZ

AA

nCBeHe 10

126

94

42

Nuclear Reactions Q values• Consider the nuclear reaction: HeCNH 4

2126

147

21

initial total mass mi : u 16.017176u 14.003074u 014102.2 final total mass mf : u 16.002602u 4.023602u 000000.12 mass difference m: u 014574.0 if mmm

The negative mass difference comes from the fact that part ofthe initial mass energy is converted into kinetic energy. The Qvalue is defined as :If the Q value is positive, the reaction is said to be exothermic reaction.

mQ

• Consider the nuclear reaction: HONHe 11

178

147

42

MeV 194.1u 001282.0 fi mmQ endothermic reaction

A careful analysis of this reaction reveals that, even if the incomingalpha particle has kinetic energy of 1.194 MeV is not enough to havethis reaction happen because, although the energy is conserved,the momentum is not. The incoming particle needs at least kineticenergy of (m/M: mass of incoming/target particle). Threshold energy

.)/1(min QMmKE