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2.5 Atomic & Nuclear Physics

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### 2.5 Atomic & Nuclear Physics

3 Credits - Internal

Rutherford’s Model of the Atom

Protons have a positive charge which is equal to the negative charge of the electron.

The neutron has no charge.

Protons and neutrons are nuclear particles called nucleons.

Rutherford’s Model of the Atom

In a stable nucleus, nucleons are bound together by very strong balanced forces.

Attraction: Nuclear Force

Repulsion: Electric Force

Rutherford’s Model of the Atom

Splitting a nucleus frees up a large amount of energy (nuclear Power)

Adding or removing electrons within their orbits (ionisation) also involves energy but much less than nuclear energy.

(chemical energy)

Composition of the Atom - Nuclides

the number of nucleons in the nucleus

Mass

Number

A

A = Z + N

Chemical

Symbol

Atomic

Number

Z

the number of protons in the nucleus

(determines the type of element)

The neutron number Nis the number of neutrons

Mass

Number

A

Examples of Nuclides:

4

20

Chemical

Symbol

He

Ne

2

10

Atomic

Number

Z

A nuclide is a symbolic way of showing mass number and atomic number

A = Z + N

Complete the following data table

isotopes

4He

14N

24Mg

32S

40Ar

38Ar

2

7

18

18

12

16

4

24

32

38

14

40

18

18

2

7

12

16

20

2

7

12

16

22

7

12

16

18

2

18

A

A = Z + N

Ch

Z

atoms of the same element that have a different number of neutrons

Electrons are arranged in orbital shells (energy levels)

The innermost shell can take up to

2 electrons.

The next two shells can take up to

8 electrons each

23

Na

11

The centripetal force holding the electrons in circular orbit is the electric force

Electrons are arranged in orbital shells (energy levels)

Radioactivity

Some elements or isotopes are less stable than others and can spontaneously emit particle or wave radiations from their nuclei

4

240

236

+

He

Pu

U

2

94

92

Nuclear Equation

Radioactivity

Conservation of Mass Number (A)

Conservation of Atomic Number (Z)

4

238

234

+

+ γ

He

U

Th

2

92

90

heavy

nucleus

new

element

alpha

particle

gamma

radiation

Radioactivity

Complete the following Nuclear Reaction Equations

214

4

218

+

He

Alpha particle

Po

Pb

2

84

82

99

99

0

+

Beta particle

Tc

Ru

β

43

44

-1

Radioactivity

Complete the following Nuclear Reaction Equations

6

1

4

9

1

+

+

He

Li

Alpha particle

Be

H

2

4

1

3

42

42

0

Beta particle

+

K

Ca

β

20

19

-1

3 Types of Radiations

4

Alpha particle α

a high speed helium nucleus

Beta particle β

a high energy electron formed when a neutron splits into a proton and an electron

Gamma wave γ

a very short wavelength (high frequency) electromagnetic wave.

He

2

0

β

-1

Ionization and Radioactivity

These radiations have the ability to ionise atoms (knock out electrons from their orbits) to produce ions

To prevent radiation, shielding of varying thickness is used

Ionization and Radioactivity

These radiations have the ability to ionise atoms (knock out electrons from their orbits) to produce ions

Alpha particleα

strong ionisers (heavy and slow) but can be stopped by paper

Beta particle β

less ionising, more penetrating (lighter, faster)

can be stopped by metal foil

Gamma particle γ

least ionising but travel quickly.

Dense materials such as concrete or lead can stop them

To prevent radiation, shielding of varying thickness is used

Ionising Radiation

Sources

These radiations are charged particles that can cause the atoms they encounter to become charged

can travel a few cm in air, absorbed by paper

particulate radiation – nucleus of He atom

4

He

High

2

up to 1 m in air, absorbed by aluminum sheet

particulate radiation

0

Med

e

-1

hardly affected by air, partially absorbed by concrete, lead

electromagnetic radiation

γ

Low

Half Life (τ or t½)

The half life of a radioactive element is the time it takes for half of the atoms in a sample to decay

Half Life

The half life of a radioactive element is the time it takes for half of the atoms in a sample to decay

0 – all nuclei are intact. Sample is most active

1 – after 1 half life (8 days), one half of the nuclei have decayed (16 g) leaving the other half intact. Radiation emitted is now half its initial level.

2 – after 2 half lives (16 days) three quarters of the nuclei have decayed (24g) leaving a quarter intact.

e.g. Consider a 32g sample of iodine – 131 with a half life of 8 days.

Half Life (τ or t½)

Result is an exponential decay curve

0 – all nulei are intact. Sample is most active (32g)

1 – after 1 half life (8 days), one half of the nuclei have decayed (16 g) leaving the other half intact. Radiation emitted is now half its initial level.

2 – after 2 half lives (16 days) three quarters of the nuclei have decayed (24g) leaving a quarter intact.

8 days

Half Life (τ or t½)

exponential decay curve

of a radioactive substance

What is the half life of this substance?

What fraction is left after 8 days?

How long does it take for 75% of this substance to decay?

What is the probability that an atom will decay in 2 days?

2 days

1/16

4 days

1/2

Half Life (τ or t½)

exponential decay curve

of a Radon-220

What is the half life of Radon-220?

What fraction is left after about 100 seconds?

How long does it take for 800 g of this sample to decay to 50 g ?

How much longer will it take this 50 g sample to decay to 12.5 g?

52 seconds

1/4

4 half lives – 208 s

2 more half lives – 104 s

Starter -Half Life

exponential decay curve of Carbon - 14

What is the half life of Carbon-14?

What fraction is left after 28,650 years?

How long does it take for 800 g of this sample to decay to 200 g ?

What is the probability an atom will decay in 17,190 years?

5730 years

1/32

2 half lives – 11,460 years

7/8

Starter

Complete the following Nuclear Reaction Equations and state what type of decay is occurring

222

4

226

+

He

Alpha Decay

Ra

Rn

2

88

86

89

89

0

+

Beta Decay

Y

Tc

e

38

39

-1

Starter – Match Terms with Descriptions

The total charge before and after a nuclear reaction remains constant

The number of particles emitted per second

An electron emitted by a radioactive nucleus

The time taken for half the nuclei in a sample to decay

An intense electromagnetic wave emitted by a radioactive nucleus

A helium nucleus emitted by a radioactive atom

The process of nuclei spontaneously breaking up and emitting particle or wave radiations

Radioactive Decay

Parent nucleus

Alpha α particle

Half Life

Activity

Conservation of charge

Beta βparticle

Gamma γ radiation

Starter -Half Life

Living plants continually absorb carbon dioxide from the air that contains a small proportion of the Carbon-14 isotope. Their radioactivity is constant whilst they are alive but declines once they die. Material derived from dead plants can therefore be dated from their activity.

a.) The Dead Sea Scrolls were dated at 100 BC. What would be the activity A measured from the parchment?

2100 years -> 11.5 particles per second

b.) The charcoal from Stonehenge had an activity A of 9.4 particles per second. How old is Stonehenge?

4000 years

c.) Carbon-14 emits beta particles to produce nitrogen. Determine the atomic and mass numbers for Nitrogen.

A

N

Z

Z = 6 + 1 = 7 A = 14

Starter -Half Life

The half-life of Plutonium-238 is 87.7 years. A sample contains 0.34 grams of Pu-234. Calculate the mass of Pu-238 that would have existed 263.1 years before the measurement was taken.

263.1/87.7 = 3 half lives

One half life ago the sample would contain 0.34 x 2 = 0.68 g of Pu-234

Two half lives ago the sample would contain 0.68 x 2 = 1.36 g of Pu-234

Three half lives ago the sample would contain 1.36 x 2 = 2.72 g of Pu-234

When will the sample of Pu-238 fall below 0.01 grams ?

2 3 4 5 6

0.17 0.085 0.0425 0.02125 0.010625 0.0053125

Starter -Half Life

The half-life of Plutonium-238 is 87.7 years. A sample contains 0.34 grams of Pu-234.

When will the sample of Pu-238 fall below 0.01 grams ?

2 3 4 5 6

0.17 0.085 0.0425 0.02125 0.010625 0.0053125

Between 5 and 6 half lives

(430.8 < t < 526.2 years)

Due to the shape of the exponential curve we see that it is closer to 5 half lives so a good estimate would be 450 years.

Nuclear Fission

The process of splitting an atomic nucleus.

Can be achieved by bombarding a nucleus with a high speed particle (usually neutrons)

e.g. an alpha particle collides with a nitrogen nucleus to produce an oxygen atom & hydrogen atom

1

4

17

14

+

+

He

O

H

N

8

7

2

1

Nuclear Fission

e.g. a chain reaction where the neutrons produced in the first fission produce further fissions

92

1

141

1

235

+

+

+ 3

n

Ba

Kr

n

U

56

92

0

0

36

Critical Mass

If one (or more) of the neutrons released in this reaction hits another uranium-235 nucleus, it will also decay. This is called a chain reaction. A radioactive substance is said to be of critical mass if there is a sufficient mass of the element for a chain reaction to occur.

92

1

141

1

235

+

+

+ 3

n

Ba

Kr

n

U

56

92

0

0

36

Nuclear Fusion

In a fusion reaction the reactants are two relatively small nuclei which fuse together to form a single, heavier, product nucleus.

17.59 Mega Electronvolts of energy

is produced in this reaction

3

4

2

1

+

+

H

He

H

n

2

1

1

0

Nuclear Fusion

Complete the following fusion reactions

3

4

2

1

+

+

He

He

H

p

1

1

2

2

6

4

2

+

2

He

H

Li

2

1

3

a-particle

g-ray

b-particle

Radioactivity in a Magnetic FieldThe 3 types of radiation behave differently in a magnetic field. α-particles carry a positive charge, β-particles carry a negative charge, so they are deflected in opposite directions when travelling through a magnetic field (right-hand-slap rule). γ rays are not charged and so are un-deflected in a magnetic field.

Compare

The splitting of a large atom into two or more smaller ones

The fusing of two or more lighter atoms into a larger one.

does not normally occur in nature.

occurs in stars, such as the sun.

Critical mass of the substance and high-speed neutrons are required.

High density, high temperature environment is required

energy released by fusion is three to four times greater than the energy released by fission.

a million times greater than that released in chemical reactions;

Fission produces many highly radioactive particles.

Few radioactive particles are produced by fusion reaction

Extremely high energy is required to bring two or more protons close enough that nuclear forces overcome their electrostatic repulsion.

Takes little energy to split two atoms in a fission reaction.

Starter

Alpha particles may be completely stopped by a sheet of ______.

________ particles can be stopped by aluminum shielding.

Gamma rays can only be reduced by much more substantial barriers, such as a very thick layer of ______ or ________.

paper

Beta

lead

concrete

How Nuclear Reactors Work

The principle behind generating electricity in a nuclear reactor is relatively simple. Atoms in the nuclear fuel undergo a chain reaction, and these reactions generate heat. The heat is used to turn water into steam. The steam turns turbines. When the turbines rotate, the power generators produce the electricity that is eventually fed into your home.

Starter - Explain

Explain why a large nucleus like uranium tends to be unstable.

Describe what the term ionise means in relation to radiation

The nucleons (protons and neutrons) are relatively far apart and so the nuclear forces binding them together tend to be weaker

Oribtal electrons are removed or added to the atom.

α-particles, β-particles, γ-rays, cosmic rays and X-rays are all forms of ionising radiation; they all have the ability to interact with matter to form ions.

Mass-Energy Equivalence

E=mc2

The mass of a body is a measure of its energy content.

The total energy before an experiment is equal to the total energy after the experiment.

E = Energy (Joules)

m = mass (kg)

c = speed of light in a vacuum

= 3.00 x 108ms-1

E=mc2

e.g.Calculate the energy released in the following fusion reaction

The total energy before an experiment is equal to the total energy after the experiment.

3

4

2

1

+

+

He

He

H

p

1

1

2

2

E = Energy (Joules)

m = mass (kg)

c = speed of light in a vacuum

= 3.00 x 108ms-1

E=mc2

e.g.c = 3.00 x 108ms-1

Calculate the energy released in the following fusion reaction

3

4

2

1

+

+

He

He

H

p

1

2

2

1

mass of reactants = 3.34330 x 10-27 + 5.0066 x 10-27

= 8.4093 x 10-27 kg

mass of products = 6.64591 x 10-27 + 1.67338 x 10-27

= 8.31929 x 10-27 kg

difference = 8.4093 x 10-27 – 8.31929 x 10-27

= 9.001 x 10-29 kg

E=mc2

e.g.c = 3.00 x 108ms-1

Calculate the energy released in the following fusion reaction

3

4

2

1

+

+

He

He

H

p

1

2

2

1

mass difference = 9.001 x 10-29 kg

E = m x (3.000 x 108)2

E = 9.001 x 10-29 x (3.000 x 108)2

= 8.1009 x 10-12 Joules

E=mc2

e.g.Calculate the energy released in the following fission reaction

The total energy before an experiment is equal to the total energy after the experiment.

1

95

4

235

137

+

+

+

Rb

He

n

Cs

U

92

0

2

55

37

E = Energy (Joules)

m = mass (kg)

c = speed of light in a vacuum

= 3.00 x 108ms-1

E=mc2

e.g.Calculate the energy released in the following fission reaction

1

95

235

137

1

+ 4

+

+

Rb

n

Cs

U

n

92

0

0

55

37

mass of reactants = 390.26689 x 10-27 + 1.67483 x 10-27

= 391.94172 x 10-27 kg

mass of prdcts = 227.4027 x 10-27 + 157.67757 x 10-27+ 4(1.67483 x 10-27)

= 391.77959 x 10-27 kg

difference = 391.94172 x 10-27– 391.77959 x 10-27

= 1.6213 x 10-28 kg

E=mc2

e.g.c = 3.00 x 108ms-1

Calculate the energy released in the following fusion reaction

1

137

235

95

1

+

+ 4

+

Cs

n

U

Rb

n

92

0

2

37

0

mass difference = 1.6213 x 10-28 kg

E = m x (3.000 x 108)2

E = 1.6213 x 10-28 kg x (3.000 x 108)2

1.45917 x 10-11 Joules

Starter

Use your periodic table to write (complete) these nuclear equations and calculate the energy released.

a.) Alpha decay of Po-218

b.) Fission reaction

4

218

214

+

He

Po

Pb

2

84

82

239

1

93

142

1

+

+

+ ?

5

Pu

n

Sr

Ba

n

94

0

38

56

0

c = 3.00 x 108

StarterUse your periodic table to write (complete) these nuclear equations and calculate the energy released.

a.) Alpha decay of Po-218

E = Δmc2

= 9.783x10-13 J

4

218

214

+

He

Po

Pb

2

84

82

mass of reactants = 361.98198 x 10-27

mass of products = 355.32520x 10-27 + 6.64591 x 10-27

= 361.97111x 10-27

difference (Δm) = 361.98198x 10-27– 361.97111 x 10-27

= 1.087 x 10-29

c = 3.00 x 108

StarterUse your periodic table to write (complete) these nuclear equations and calculate the energy released.

a.) Alpha decay of Po-218

E = Δmc2

= 2.786x10-11 J

1

142

1

239

93

+

+

+ 5

n

Ba

n

Pu

Sr

0

56

0

94

38

mass of reactants = 396.92935x 10-27 + 1.67483 x 10-27

mass of products = 154.27837x 10-27 + 235.64216x 10-27+ 5(1.67483 x 10-27)

= 398.29468 x 10-27

difference (Δm) = 398.60418 x 10-27– 398.29468 x 10-27

= 3.095 x 10-28

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