A nucleus of an atom is made up of protons and neutrons that known as nucleons (is defined as the particles found inside the nucleus).

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1 Chapter 11: Nucleus 11.1 Properties of Nucleus State the properties of proton and neutron nucleus of an atom is made up of protons and neutrons that known as nucleons (is defined as the particles found inside the nucleus). Proton and neutron are characterized by the following properties: Charge (C) Proton (p) Neutron (n) Positive charge (+e) No charge x Mass (kg) Mass (u) Define proton number, nucleon number, neutron number and isotopes Proton number Definition: the number of protons in the nucleus. lso called as atomic number Symbol : Z Neutron number Definition: the number of neutrons in the nucleus. Symbol : N Relationship = Z + N Nucleon number Definition: the total number of neutrons and protons in the nucleus. lso called as atomic mass number Symbol : Isotope Definition: the atoms of the same element whose nuclei contain the same number of protons (Z) but different number of neutrons (N). Example : 1 3 1H, 1H, 1H (Hydrogen, deuterium, tritium) 1

2 State to represent a nuclide The atomic nucleus can be represented as Z X where X = symbol for the element Example Z = atomic number (number of protons) = atomic mass number = total number of protons and neutrons Question What is meant by the following symbols? 1 0 n p e State the mass number and sign of the charge for each entity above. Example Element : Iron-56 Proton no, Z : 6 Nucleon no, : 56 Neutron : 56-6 = 30 - Z = N Solution Element nuclide Number of protons Number of neutrons Number of electrons 1 1H 9 4 Be 14 7 N 16 8O 3 11 Na 59 7 Co 31 16S Cs U Binding Energy and Mass Defect Einstein Mass-Energy Relation From the theory of relativity, it leads to the idea that mass is a form of energy.

3 Mass and energy can be related by the following relation: E mc where E : amount of energy m : rest mass (must be in kg) c : speed of light in vacuum Unit conversion of mass and energy The electron-volt (ev) Is a unit of energy Is defined as the kinetic energy gained by an electron in being accelerated by a potential difference (voltage) of 1 volt. 1eV MeV ev The atomic mass unit (u) Is a unit of mass Is defined as exactly the mass of a neutral carbon-1 atom. mass of 1u 1 1u C 7 kg 1 atomic mass unit (u) can be converted into unit of energy by using the massenergy relation: In joule: 1u In ev/c or MeV/c : E mc E ev/c MeV/c Define and determine mass defect Mass defect is defined as the difference between the sum of the masses of individual nucleons that form an atomic nucleus and the mass of the nucleus. 3

m Zm p Nmn M where m p : mass of proton m n : mass of neutron M : mass of nucleus Z : number of proton N : number of neutron The mass of a nucleus (M ) is always less than the total mass of its

4 m Zm p Nmn M where m p : mass of proton m n : mass of neutron M : mass of nucleus Z : number of proton N : number of neutron The mass of a nucleus (M ) is always less than the total mass of its constituent nucleons (Zm p + Nm n ): M Zm p Nm The reduction in mass arises because the act of combining the nucleons to form the nucleus causes some of their mass to be released as energy. ny attempt to separate the nucleons would involve them being given this same amount of energy. The energy is called the binding energy of the nucleus. n 11.. Define and determine binding energy and binding energy per nucleon Energy required to separate a nucleus into its individual protons and neutrons. OR Energy released when nucleus is formed from its individual nucleons. The binding energy of the nucleus is equal to the energy equivalent of the mass defect. Hence E B mc where E B : amount of energy Δm : rest mass c : speed of light in vacuum There are methods to determine the value of Binding Energy, E B : E B in unit joule Δm in unit kg E B in unit MeV Δm in unit u c = m s Describe graph of binding energy per nucleon against nucleon number Binding energy per nucleon is defined as mean (average) binding energy of a nucleus. It is a measure of the nucleus stability where 4

Binding energy, E Binding energy per nucleon B Nucleon number, mc Binding energy per nucleon Graph of binding energy per nucleon against nucleon number For light nuclei the value of E B / rises

5 Binding energy, E Binding energy per nucleon B Nucleon number, mc Binding energy per nucleon Graph of binding energy per nucleon against nucleon number For light nuclei the value of E B / rises rapidly from 1 MeV/nucleon to 8 MeV/nucleon with increasing mass number. For the nuclei with between 50 and 80, the value of E B / ranges between 8.0 and 8.9 MeV/nucleon. The nuclei in this range are very stable. 6 The nuclide 8 Ni has the largest binding energy per nucleon ( MeV/nucleon). For nuclei with > 6, the values of E B / decreases slowly, indicating that the nucleons are on average, less tightly bound. For heavy nuclei with between 00 to 40, the binding energy is between 7.5 and 8.0 MeV/nucleon. These nuclei are unstable and radioactive. Example Question Solution Calculate the binding energy of an aluminum 5

6 7 nucleus 13 l in MeV. (Given mass of neutron, m n = u ; mass of proton, m p = u ; speed of light in vacuum, c = m s -1 and atomic mass of aluminum, M = u) Calculate the binding energy per nucleon of a 10 boron nucleus 5 B in /nucleon. Given atomic mass of boron, M = u. Exercise Question Calculate the binding energy in joule of a deuterium nucleus. The mass of a deuterium nucleus is kg. nswer: Calculate the average binding energy per nucleon of the nitrogen-14 nucleus 7 N. Given atomic mass of nitrogen-14 atom = u nswer: 7.47 MeV/nucleon 6

UNIT 15: NUCLEUS SF027 1

UNIT 15: NUCLEUS SF027 1 is defined as the central core of an atom that is positively charged and contains protons and neutrons. UNIT 5: NUCLUS SF07 Neutron lectron 5. Nuclear Structure nucleus of an atom is made up of protons