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26.1 Properties of nucleus26.2 Binding energy and mass defect.

UNIT 26 : NUCLEUSis defined as the central core of an atom that is positively charged and contains protons and neutrons.

(2 HOURS)

At the end of this topic, students should be able to:

State the properties of proton and neutron Define

◦ Proton number◦ Nucleon number◦ Isotopes

Use to represent a nuclide

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26.1 Properties of nucleus (1/2 Hour)

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26.1 Properties of nucleus• A nucleus of an atom is made up of protons and neutrons that is also known as nucleons.

Figure 26.1.1( atom) Figure 26.1.2 (nucleus)

Proton Particle with positive charge of the nucleus Charge : +1.60 x 10-19 C Mass : 1.672 x 10-27 kg / 1.007276 u

Neutron Particle with no charge of the nucleus Charge : - Mass : 1.675 x 10-27 kg / 1.008665 u

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26.1.1 Properties of proton and neutron

Proton number Definition: the number of protons in the nucleus. Also called as atomic number Symbol : ZNucleon number Definition : the total number of neutrons and protons in

the nucleus. Also called as atomic mass number Symbol : AIsotope Definition : the atoms of the same element whose nuclei

contain the same number of protons (Z) but different number of neutrons (N).

Example : (Hydrogen, deuterium, tritium)

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1 2 31 1 1H, H, H

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The atomic nucleus can be represented as

XAZ

where X = symbol for the elementZ = atomic number (number of protons)A = atomic mass number = total number of protons and neutrons

Example :

5626 Fe Element : Iron-56

Proton no, Z = 26Nucleon no, A = 56Neutron = 56-26 = 30

A - Z = N

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Element nuclide

Number of protons

Number of neutrons

Number of electrons

8 8 8

H11

N147

Na2311

Co5927

Be94

O168

S3116

Cs13355

U23892

Example 26.1

Complete the table below:

At the end of this topic, students should be able to:

Define and determine mass defect Define and determine binding energy,

Identify the average value of binding energy per nucleon of stable nuclei from the graph of binding energy per nucleon against nucleon number.

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26.2 Binding energy & Mass Defect (1 1/2 Hour)

26.2.1 Mass defect, Δm

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Definition

the difference between the sum of the masses of individual nucleons that form an atomic nucleus and the mass of the nucleus.

Formula Anp MNmZmm Δ

proton a of mass: pm

nucleus a of massAM

neutron a of mass: nm

neutrons of number

protons of number

N

Z

Example 26.2

From example above, can you determine the value of mass defect ? (Ans : 0.040475 a.m.u)

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26.2.2 Binding Energy, EB

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Definition

Energy required to separate a nucleus into its individual protons and neutrons.

@ Energy released when nucleus is formed from its individual nucleons.

Formula

Where E : Binding energy Δm : Mass defect c : speed of light = 3.00 x 108ms-1

There are 2 methods to determine the value of Binding Energy, EB

Example : Let Δm = 1 u = 1.66 x 10-27kg

=

Note : 1eV = 1.6 x 10-19J

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EB ( in unit J )

Δm ( in unit kg )

c = 3.00 x 108ms-1

EB ( in unit MeV )

Δm ( in unit u )

2 931.5MeVc =

u

2B

-27 8 -1 2

-10 2 -2

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E = Δmc

=(1.66×10 kg)(3.00×10 ms )

=1.4904×10 kgm s

=1.4904×10 J

2BE = Δmc

931.5MeV=(1 u)

u

=931.5MeV

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Example 26.3

Calculatea) mass defect andb) binding energy of the deuterium. Given

Solution:

21 mass 2.013553 uH

Calculate binding energy of the Helium nucleus, in SI unit.Given mass of helium atom = 4.002603 u

Solution:

14

Example 26.4

42 He

26.2.3 Binding Energy per nucleon,

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Definition mean (average) binding energy of a nucleus

Binding energy per nucleon is measure the stability of of the nucleus.

The greater the binding energy per nucleon, the more stable the nucleus is.

BE

N

)number(Nucleon

)(energy Bindingnucleonper energy Binding B

A

E

A

mc2

nucleonper energy Binding

16Mass number A

Bin

din

g e

ner

gy

per

nu

cleo

n (

MeV

/nu

cleo

n)

Greatest stabilityBinding energy per nucleon as a function of mass number,A

For light nuclei the value of EB/A rises rapidly from 1 MeV/nucleon to 8 MeV/nucleon with increasing mass number A.

For the nuclei with A between 50 and 80, the value of EB/A ranges between 8.0 and 8.9 Mev/nucleon. The nuclei in these range are very stable.

The nuclide has the largest binding energy per nucleon (8.7945 MeV/nucleon). For nuclei with A > 62, the values of EB/A decreases

slowly, indicating that the nucleons are on average, less tightly bound.

For heavy nuclei with A between 200 to 240, the binding energy is between 7.5 and 8.0 MeV/nucleon.These

nuclei are unstable and radioactive.

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From the graph:

Ni6228

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Example 26.5

Calculate the average binding energy per nucleon of the iron-56 .

Given

Solution:

Fe5626

u 1.00867 mass

u 1.00782 mass

u 55.93494mass

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11

n

pH

Fe11

5626

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Exercise1) The binding energy of the neon is160.64 MeV.

Find its atomic mass. Given

(Ans: 19.992u)

2) Determine the total binding energy and the binding energy per nucleon for the nitrogen -14 nucleus

Given

(Ans:104.6 MeV,7.47 MeV/nucleon)

N147

u 1.008665 mass

u 1.007825 mass

u 14.003074mass

10

11

n

pH

N11

147

Ne2010

u 1.008665 mass

u 1.007825 mass 10

n

p11

3) Calculate the binding energy of an aluminum nucleus in MeV.

(Given mass of neutron, mn=1.00867 u ; mass of proton, mp=1.00782 u ; speed of light in vacuum, c=3.00108 m s1

and atomic mass of aluminum, MAl=26.98154 u)

(Ans: 225 MeV)

4) Calculate the binding energy per nucleon of a boron nucleus in J/nucleon.

(Given mass of neutron, mn=1.00867 u ; mass of proton, mp=1.00782 u ; speed of light in vacuum, c=3.00108 m s1 and atomic mass of boron, MB=10.01294 u)

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(E = 1.04x10 -12 J/nucleon)

5) Why is the uranium-238 nucleus is less stable than carbon-12 nucleus? Give an explanation by referring to the binding energy per nucleon.

(Given mass of neutron, mn=1.00867 u ; mass of proton, mp=1.00782 u ;

speed of light in vacuum, c=3.00108 m s1; atomic mass of carbon-12, MC=12.00000 u and atomic mass of uranium-238, MU=238.05079 u )

(Ans: U think)

The end…..Next chapter : nuclear

reaction

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