Nuclear Physics and Radioactivity

Vocabulary

alpha particle - positively charged particle consisting of two protons and two neutrons. (Helium nucleus)

atomic mass number (A) - the number of protons and neutrons in the nucleus of an atom.

atomic mass unit - the unit of mass equal to 1/12 the mass of a carbon-12 nucleus; the atomic mass rounded to the nearest whole number is called the mass number.

atomic number (Z) - the number of protons in the nucleus of an atom.beta particle - high speed electron emitted from a radioactive element

when a neutron. decays into a protonbinding energy – the energy required to completely separate the nucleus

into its individual protons and neutrons.element - a substance made of only one kind of atom.isotope - a form of an element which has a particular number of neutrons,

that is, has the same atomic number but a different mass number than the other elements which occupy the same place on the periodic table.

Vocabulary

mass defect - the mass equivalent of the binding energy in the nucleus of an atom by E = mc2

neutron - an electrically neutral subatomic particle found in the nucleus of an atom

nuclear reaction - any process in the nucleus of an atom that causes the number of protons and/or neutrons to change

nucleons - protons or a neutronsstrong nuclear force - the force that binds protons and neutrons together

in the nucleus of an atomtransmutation - the changing of one element into another by a loss of gain

of one or more protons

Equations and symbols

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ΔE = Δm( )c 2

1u =1.66x10−27 kg = 931MeVc−2 XAZ

where ΔE = binding energy of the nucleusΔm = mass defect of the nucleusc = speed of light = 3 x 108 m/su = atomic mass unitX = element symbolA = atomic mass number (number of protons and neutrons)Z = atomic number (number of protons)

H11

n10

e01

Particle Symbol Relative mass Charge Location

proton1 +1 nucleus

neutron1 0 nucleus

electron or e- 0 -1electron orbitals

around the nucleus

Find the number of protons, electrons and neutrons in a neutral atom of iron.

Fe5626

# protons

# protons + #neutrons

26 protons

30 neutrons

neutral → #protons = # electrons = 26

M2M1

Before After

M 5

M4

M3

Eo Ef=<Mo Mf=>

Eo = Ef + (Mo-Mf)c2

Eo = Ef + (Δm)c2

MASS is transferred to ENERGY

N147 p

ppppppn nn

nn

n n

N147

ppppppp

n nnn

nn n

Mass defect is responsible for the binding energy. Ebinding = (Δm)c2

Calculate the binding energy of Nitrogen. The atomic mass of Nitrogen is 14.003074 u.

Nucleon Mass (u)

Proton 1.00782

Neutron 1.00866

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714N

7 protons7 neutrons

Mass of individual protons and neutrons7(1.00782u) + 7(1.00866u) = 14.11536u

Δm = 14.11536u – 14.003074u = .112286u

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.112286u ×931MeVc−2

1u=105MeVc−2

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E = Δm( )c 2 = 105MeVc−2( )c

2 =105MeV

Transmutation of nitrogen into carbon

714N0

1n 614C

Nuclide/particle Mass (u)

14.003074

neutron 1.008664

14.003241

proton 1.007825

14 N

14C

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11H

Mass of products14.003074u + 1.008664u = 15.011738u

Mass of reactants14.003241u + 1.007825u = 15.011066u

Δm = 15.011738u – 15.011066u = .000672u

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.000672u ×931MeVc−2

1u= 0.626MeVc−2

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E = Δm( )c 2 = 0.626MeVc−2( )c

2 = 0.626MeV

Nuclear fusion – The joining of two small nuclei to form one large nucleus. The mass of the smaller nuclei is greater than the mass of the large nucleus. High temperatures are required for fusion. Example: the sun

Nuclear fission – Splitting a large nucleus into two smaller nuclei. The mass of the large nucleus is greater than the two smaller nuclei. Example: Nuclear power plant

In both cases the mass of the products is less than the mass of the reactants, which results in a mass defect. The mass is converted to energy according to the equation E = (Δm)c2

Binding energy per nucleon vs. mass number

Binding energyPer nucleon

(MeV)

Mass number

Iron (Fe) staple

fusi

onFission

Fusion Examples:

Nuclide Mass (u)

1.007825

2.014101

3.016049

3.016029

4.002603

1.008664

1 H

3He

3 H

2 H

4Hen1

0

12H1

3H 24He0

1n

12H1

2H 23He0

1n

12H1

2H 13H1

1p

12H2

3He 24He1

1p

Nuclide Mass (u)

1.007825

2.014101

3.016049

3.016029

4.002603

1.008664

1 H

3He

3 H

2 H

4Hen1

0

12H1

3H 24He0

1n

Mass of reactants2.014101u + 3.016049u = 5.03015u

Mass of products4.002603u + 1.008664u = 5.011267u

Δm = 5.03015u – 5.011267u = .018883u

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.018883u ×931MeVc−2

1u=17.5MeVc−2

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E = Δm( )c 2 = 17.5MeVc−2( )c

2 =17.5MeV

Fission Example: absorbs a neutron and splits into and , Write the equation for the nuclear reaction and calculate the energy released in this reaction.

U23692 Mo100

42

Sn12650

Z symbol A Mass (u)

92 U 236 236.045563

42 Mo 100 99.907476

50 Sn 126 125.907653

Fission Example: absorbs a neutron and splits into and , Write the equation for the nuclear reaction and calculate the energy released in this reaction.

U23692 Mo100

42

Sn12650

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92236U +0

1 n→42100 Mo +50

126 Sn + neutrons

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92236U +0

1 n→42100 Mo +50

126 Sn + ? 01n( )

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92236U +0

1 n→42100 Mo +50

126 Sn +11 01n( )

Z symbol A Mass (u)

92 U 236 236.045563

42 Mo 100 99.907476

50 Sn 126 125.907653

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92236U +0

1 n→42100 Mo +50

126 Sn +11 01n( )

Mass of products236.045563u + 1.008664u = 237.054227

Mass of reactants125.907653u + 99.907476u + 11(1.008664u) = 236.910433u

Δm = 237.054227u – 236.910433u = .143794u

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.143794u ×931MeVc−2

1u=134MeVc−2

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E = Δm( )c 2 = 134 MeVc−2( )c

2 =134MeV

Radioactivity – Particles are randomly emitted from an unstable nucleus in order to become more staple. These are the different particles emitted.

β+positron

High Energy

Photonsgamma

β-Beta

αAlpha

symbolName

He42

e01

e01

Nuclear Equations:

nPAl 10

3015

2713?

pn 11

10

?23491 PaTh

ThU23892

Nuclear Equations:

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92238U→ Th + α

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92238U→ Th+2

4He234

90

Alpha decay

Nuclear Equations:

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90234Th→ 91

234 Pa + ?

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23490Th→ 91

234 Pa+−10e

-1

0

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23490Th→ 91

234 Pa + Β−

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+ν

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ν = anti - neutrino

Bet

a de

cay

Nuclear Equations:

nPAl 10

3015

2713? 4

2

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24He+13

27Al→1530 P+0

1n

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+1327Al→15

30 P+01n

Transmutation

Nuclear Equations:

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01n→1

1 p + ?

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01n→1

1 p+−10e

-10

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01n→1

1 p + Β−

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01n→1

1 p + Β− +ν So a neutron is the combination of a proton and an electron